An Integrated Computational Materials Engineering Predictive Platform for Fatigue Prediction and Qualification of Metallic Parts Built With Additive Manufacturing

Additive manufacturing (AM) is defined as the “process of joining materials to make parts from three-dimensional (3D) model data, usually layer upon layer, as opposed to conventional manufacturing (CM) including subtractive manufacturing technologies and formative manufacturing methodologies” [1]. AM provides significant advantages over conventional manufacturing processes, such as allowing fabrication of complex structures, significantly reduced material usage, and shortened product development cycles. The market size of AM has increased significantly with ∼20% compound annual growth rate in the past 15 years, and an even faster growth rate is projected in the next 10 years. The current market size is ∼$12B and is estimated to increase to ∼$120B by 2029 [2].

Materials used in AM processes can have a variety of forms, including powder, liquid, wire, sheet, and so on. Among those forms, powder-based additive manufacturing processes are the most widely used at an industrial level. The application of powder-based AM spans across aerospace, defense, medical device, automotive, molds and dies, and other industries. In recent years, metal additive manufacturing has gained increasing attention and adoption for production of high-end components. As an example provided in Ref. [3], in 2015 GE started the series production of fuel nozzles for its LEAP engines using AM. According to GE, the AM technology enables them to produce the fuel nozzle in a single piece rather than 20 pieces welded together using traditional manufacturing processes. The new fuel nozzle has 25% less weight, 30% more efficiency, and is five times more durable than its predecessor.

Along with the significant opportunities and advantages offered by metal additive manufacturing, there are several challenges that need to be addressed before metal AM gets wider implementation in commercial sectors. Process-induced defects present significant challenges for additively manufactured parts. Various types of defects arise in AM processes, such as porosity, unmelted particles, grain anisotropy, balling effects, material inhomogeneity, residual stress, and distortion [4]. The cyclic and rapid heating/cooling phenomenon in AM processes modifies the microstructure, but the mechanism is not well understood due to the complexity in nonequilibrium conditions. Process parameters need to be tailored for different materials and geometries and to be tightly controlled to produce high-quality parts. AM part qualification is another big challenge. The traditional approach for part qualification is rooted in physical testing. This typically requires thousands of tests to create a reliable database and costs millions of dollars and years to complete. Additionally, any changes in AM processes, machines, or materials will require a re-qualification process. Leveraging advanced simulation and high-performance computing provides a pathway to achieving rapid part qualification for AM components.

As exciting as the potential for AM technology is, there are obstacles to achieving the full realization of the benefits that are expected from broad implementation of AM designs and products. The following is directly from the SEP 2015 Quadrennial Technology Review (QTR) [5], addressing two of the most pressing challenges facing the Additive Manufacturing community (it should be noted that DCAM is qualified to address these issues). From QTR appendix [5] on Additive Manufacturing:

• “Validation and demonstration: Manufacturers, standards organizations, and others maintain high standards for critical structural materials, such as those used in aerospace applications. Providing a high level of confidence in the structural integrity of components built with additive technology may require extensive testing, demonstration, and data collection. The cost to establish material properties for each material, to each additive process, and to a lesser extent each machine, can exceed many thousands of dollars (and millions in critical applications)—a huge barrier to entry.”

• “Modeling: Modeling and simulation of AM enables the design and implementation of process control methods. Physics-based process models are needed to understand the fundamental physics of AM processes, both for current single material processes and especially for multi-material additive processes, where interface issues, such as bonding and thermal expansion, can present significant issues.”

Despite the substantial benefits of incorporating AM, the process can be difficult to optimize. For highly technical or safety-critical industries (such as aerospace), it will usually take dozens or even hundreds of attempts to optimize a new part design and achieve acceptable qualification (life expectancy results). The refinement of AM process parameters to maximize life is a highly iterative process that is time- and resource-intensive, and it limits the number of new designs/applications that a manufacturer can bring to the market in a timely manner. This is a critical limiting factor in the ability of industry leaders like aerospace original equipment manufacturers (OEMs) to truly exploit the capability. Companies in industries such as aerospace are eager to move forward with disruptive new AM designs, but there is a gap in the current market’s ability to move quickly to optimize AM build parameters and qualify AM components.

Feedback from several aerospace OEMs indicates that they internally forecast a requirement to build approximately 25–50 samples before they can identify the optimal combination of process parameters to reliably produce a part with enough life expectancy for an aerospace application. Depending on AM machine availability, this can result in an optimization/qualification process for each new design that takes weeks or months and costs tens of thousands of dollars. In addition, this slows the go-to-market process and affects the ability to rapidly implement valuable weight-reducing and performance-enhancing capabilities of AM components. Our modeling tool has the capability to:

• Reduce prototype optimization sample builds from dozens to just a handful.

• Accelerate process and part qualification timelines from weeks/months to days.

• Enable faster implementation of AM-based designs.

Additive manufacturing technology is gaining attention in tribological applications where product performance is strongly linked to the near-surface mechanical properties and surface finish of components. As the array of suitable materials grows and build processes improve, AM is enabling unique, functional solutions for specialized applications in the aerospace, automotive, and biotech industries that are not possible with conventional manufacturing methods.

Engineered scaffolding for cell cultures has become a promising area of research in tissue engineering [6]. It is important that the scaffolds closely mimic the natural architecture and porosity of the extracellular matrix to promote proper integration and functioning with human cells. Though they are typically made of polymers, metallic foams are a new class of materials under consideration. For instance, surfaces of artificial hip replacement stems can be fabricated from Ti6Al4V by electron beam melting (EBM) to produce the required stiffness, three-dimensional topography, and porosity to provide adequate load support and enhanced cellular adhesion [6].

Makers of power transmission machines and components for the automotive and aerospace industries are also turning to AM technology for prototyping and small batch production [7,8]. For vehicles with mechanical drivetrains, AM provides a new means to realize improvements in efficiency and reliability. Additive manufacturing enables production of parts with complex shapes optimized for weight, inertia, and stiffness, and it also enables the integration of bearing and gear components with other elements of a vehicle powertrain. Reference [9] achieved >13% weight reduction in a combined differential housing and ring gear using laser powder bed fusion of 20MnCr5 (a medium strength case-hardenable steel) for a conventional front transverse transmission. In another example, an aluminum wire-race bearing was topologically optimized to meet stringent weight requirements for a helicopter application; an impossible feat for conventional manufacturing techniques due to the resulting complex lattice structure that was generated [10]. Apart from weight-saving opportunities, bearing components can benefit from the opportunity AM affords to build in functionally graded material properties to reduce part count and simplify assembly. For instance, some large-diameter rolling bearings are constructed from high-strength aluminum alloy rings for weight savings, but the wear resistance of this material is insufficient for proper functioning of the rolling surfaces. Hardened steel wires seated in the rings serve as the wear-resistant surfaces contacted by the rolling elements. Alternatively, a unibody component can be made by laser metal deposition using a dual-powder feed that blends hard particle reinforcement (spherical fused tungsten carbide) into the matrix material (EN AW-7075) when building the near-surface material to achieve appropriate hardness for the raceway surface [11].

In this paper, we present the development of DigitalClone for Additive Manufacturing (DCAM), an Integrated Computational Materials Engineering (ICME) tool for simulation of AM process and materials, and for prediction of the behavior and performance of AM components. First, the fundamentals of the three main modules of DCAM (i.e., process modeling, microstructure modeling, and fatigue modeling) are reviewed. In order to demonstrate the applicability of this tool for different geometries and materials, a series of experimental validations on multiple AM coupon samples with different geometries, materials, and loading conditions are presented. Also, the material characterizations of these samples are briefly reviewed.

Described here is the development of a modeling tool enabling prediction of the performance of parts built with AM, with rigorous consideration of the microstructural properties governing the nucleation and propagation of fatigue cracks. This tool (DCAM) is an ICME tool that includes models of crack initiation and damage progression with the high-fidelity process and microstructure modeling approaches. The predictive model has three main modules: process modeling, microstructure modeling, and fatigue modeling. Figure 1 shows the relationships between these modules and the input and output parameters of each module. In Sec. 2, a detailed description and theoretical basis of each module is provided.

Residual stress and distortion are the primary causes of printing failures, such as part warping, cracking, or recoater jams. As a result, industrial OEMs currently invest heavily in design and process optimization to prevent such defects. Experimental trial-and-error iterations are very expensive and time consuming. Computational tools hold the promise of reducing the time and cost to develop AM processes by reducing the required experimental iterations. However, simulation of part-level distortion is very challenging using traditional finite element analysis (FEA) because the layer-by-layer building process requires the simulation of hundreds of thousands of scans, which is highly impractical. New approaches for part-level simulation have been widely explored in literatures [12–21]. Among those approaches, “inherent-strain” method has proven to be an efficient way to simulate part-level distortion and residual stress. As such, DCAM implements generic “inherent-strain” method in its multi-scale modeling framework for part-level process modeling. The workflow of the multi-scale modeling framework is shown in Fig. 2.

At the micro-scale, a two-step FEA model is used to simulate the temperature evolution and thermal stress for a few scans and layers. In the thermal model, the energy source is represented by a physics-based model of heat flux that considers power, scan speed, and hatch spacing. Temperature-dependent and material state-dependent properties are incorporated in the simulation so the heat transfer phenomenon in the AM process can be accurately captured. A mechanical analysis is then conducted to simulate the thermal stress/strain induced by the temperature gradient, and the inherent strain tensor is obtained. In the meanwhile, the temperature evolution from thermal modeling at micro-scale will be past into microstructure model for solidification modeling.

At the macro-scale, the part is partitioned into lumping layers along the build direction. One lumping layer comprises several physical layers. The lumping layers are activated one-by-one, and the inherent strain is applied sequentially. The bottom of the build plate is fixed during the simulation. This process modeling implementation has been validated against experiments for various materials (e.g., IN718, IN625, 15-5SS, etc.) and shows high predictive accuracy (see Sec. 3.5 for an example).

DCAM implements a finite element–cellular automata (FE-CA) model to simulate microstructure evolution. Figure 3 illustrates the simulation workflow of the microstructure modeling temperature evolution within an AM build process. Then, the temperature history of a selected cross section is projected to a two-dimensional (2D) CA domain with refined grid size. Finally, solidification behavior is simulated using the CA method. Details of the FE and CA models are provided below. It should be noted that the illustration in Fig. 3 is only for demonstration of FE-CA method. In actual DCAM simulation, certain finite element analysis (i.e., temperature evolution) results will be imported from process module for cellular automata modeling of solidification process.

The cellular automata (CA) method is based on an algorithm to describe discrete spatial and temporal evolution of a system. This method was first applied to simulate the microstructure formation in solidification [22]. Since then, the CA method has been widely adopted by many researchers to model grain structure formation in different solidification processes, including casting, welding, additive manufacturing, etc. [23–28]. Compared, with other microstructure modeling methods (e.g., phase field method, Monte Carlo method), the CA method has the advantage of good computational efficiency while still maintaining the physics-based algorithm in the modeling.

In the simulation, the temperature profile at each time-step is mapped from the finite element method model into the CA domain, and the temperature at each CA cell drives the grain nucleation and growth.

Grain nucleation in the melt pool is an important characteristic that determines the final grain size and morphology. Pure epitaxial growth without grain nucleation results in columnar dendritic grains in rapid solidification, while heterogeneous grain nucleation in the melt pool leads to mixed columnar and equiaxed grain structures. The current microstructure model implements Thevoz’s statistical model [29] that accounts for heterogenous nucleation in solidification (Eq. (3)). The model describes the heterogeneous nucleation sites as a function of undercooling temperature

In addition to grain structure modeling, the current microstructure model also accounts for porosity via correlating the temperature history. As described in thermal modeling, the heat flux model can be customized to fit different heat sources. As such, the thermal model can predict accurate melt pool dimensions, which can be correlated with lack-of-fusion porosity. At the same time, the model also correlates keyhole/boiling porosity with melt pool areas whose temperature is above material boiling temperature. In this scenario, statistical porosity coefficients are incorporated in the model in order to account for the stochastic nature of pore formation. It is noted that those porosity coefficients need to be calibrated for each combination of AM machine and material.

In the fatigue modeling module, the part geometry, fatigue loading, material properties, and material microstructure generated in the previous module are used collaboratively to predict the fatigue behavior and fatigue life of the component. This module uses the Component Life Prediction framework [32]. This framework has been developed and validated under several SBIR projects. To achieve the previously-mentioned goal, the framework utilizes the following steps:

1. Macro-level load (global FEA) analysis: In this step, the entire geometry of the component under consideration is meshed and subjected to fatigue loading conditions. The goal is to identify the hot zones (areas with highest stresses or user-defined desired areas) for further detailed fatigue analysis. In this step, a representative volume element (RVE) is selected in the hot zone, and the output of this step are the internal stresses that are applied to this RVE due to the geometry and fatigue loading applied to the entire component. It should be noted that this RVE is selected because it is computationally intensive to perform fatigue damage analysis on an entire component. As mentioned, this sub-model RVE represents the high-stress regions (critical sites for crack initiation) in the global FE model.

2. Material properties input: In this step, different material inputs are provided to the model, including

   • – Bulk material properties: Young’s modulus, Poisson’s ratio (normally available in the literature and material catalogs)

   • – Microscale material properties: specific fracture energy per unit area, internal frictional stress (described in more details later) (these needs to be measured and calculated experimentally)

   • – Surface roughness (measured experimentally)

   • – Residual stress profile (measured experimentally or predicted by simulation)

3. Micro-level fatigue damage modeling: In this step, the internal stress and residual stress profiles are used to load the RVE material microstructure model to perform micro-stress analysis at the grain level and update micro-stress fields as fatigue damage accumulates. In DCAM, the damage accumulation, crack nucleation, and early propagation are governed by damage mechanics theories and not by fracture mechanics theories. For this purpose, Tanaka-Mura dislocation theory [33] is used:

   $Ni=4GWG(Δτ−2Mk)2(1−υ)d$

   (5)

   where W_G is the specific fracture energy per unit area, d is the grain size, G is the shear modulus, v is the Poisson’s ratio, k is the internal frictional stress, Δτ is the average resolved shear stress range, and N_i is the number of cycles required to initiate a crack on a grain boundary. This modeling approach is capable of estimating fatigue damage on a cycle-by-cycle basis to provide accurate life analysis. The number of cycles to crack initiation and propagation is calculated using stress field data at the nodal points of the mesh in the RVE microstructure model. As seen, the Tanaka-Mura model connects the material properties (both macro-level and micro-level) and internal stresses (projected on the grain boundaries) to calculate micro-level fatigue damage accumulations and correspondingly the incremental life values.

4. Iterative updating of internal stress field and recalculation of accumulated fatigue damages: as the internal fatigue damage is accumulated at the grain level and micro-cracks are created at the grain boundaries, the internal stress field needs to be recalculated. This recalculated stress field along with continuation of applied fatigue loading introduces new fatigue damage accumulation at the grain level (which needs to be calculated using the previous step).

5. Final failure: the iterative process of steps 3 and 4 are repeated until a final failure happens resulting in the total fatigue life at the end of simulation. It should be noted that this final failure can be a user-defined condition (like a certain number of cycles has been reached, or a specific crack length has been created), or a preset condition in the model (like static failure when the domain cannot stand the loading anymore and fails immediately, the crack has gone through the entire domain and causing catastrophic failure, or the crack has stopped growing resulting in infinite life).

6. Statistical analysis: fatigue by nature is a random phenomenon, i.e., under the same fatigue loading conditions the seemingly similar components built from the same material fail at different times. This is due to the micro-level variations in material microstructure. To capture the random nature of fatigue, different RVEs are generated (in microstructure module) for each fatigue modeling simulation to capture the variability in material microstructure, properties, and surface finish. This provides a fatigue life distribution that can be displayed as a Weibull plot (for a single applied load) or an strain-life and stress-life (S-N) curve (for multiple applied loads).

In this section, the applicability of DCAM tool for different geometries and materials is demonstrated through a series of experimental validations and material characterizations on multiple AM coupon samples with different geometries, materials, and loading conditions. For a complete analysis and validation for each example, the following pieces need to be performed:

• – Perform process simulation

• – Perform microstructure simulation

• – Perform fatigue simulation

• – Perform physical material characterization

• – Perform physical material validation

• – Perform physical fatigue testing

As mentioned above to show the applicability of the model, we are going to present multiple examples. For this purpose, we present the examples on the materials that are widely accepted and used in AM industries. However, providing details on all of above steps for all of these examples will make the current paper very long and exhausting. Also, the approach and steps are similar for different materials just with different results based on the material. Therefore, as we present the following examples of applicability and validation of DCAM framework, we show only a selection of the analysis and results for each example. In order for the reader to track the desired information more easily, we have prepared Table 1 to summarize the different information that is provided for each example.

Cube coupons were built using an EOS M290 laser powder bed fusion machine using five different energy densities as shown in Table 2. Among those parameters, sample #C is built using the vendor default parameter set—its nominal energy density is considered 100%. Other samples (A, B, D, E) were built using different energy densities by varying laser power and/or scan speed in order to create “artificial” defects. Each parameter was repeated three times to reduce experimental error.

After the samples were built and cutoff from the build plate, both optical microscopy and X-ray computed tomography (CT) were used to characterize the porosity. Figure 6 shows the optical microscopy images of five samples. Samples were ground using SiC paper down to 1200 grit and then polished using diamond suspension which started at 9 µm and finished at 0.5 µm. Final polishing was performed using 0.02 µm colloidal silica. The images show that Sample A and Sample B have irregularly shaped pores. This is because of the lack of fusion at a low energy density condition. Sample D and Sample E have spherical pores that are different from Samples A and B. This is because high energy density causes boiling or keyhole pores that are different from pores due to lack-of-fusion. Sample C has the minimum porosity as it was built at a near-optimal laser energy density. Figure 7 shows the representative image from an X-ray CT scan and the overall porosity level from five different energy densities. The average porosity value aligns with the observation in Fig. 6. From low energy density levels, porosity decreases with increasing the energy density up to near optimal value, while at high energy density levels, porosity increases with increasing energy density.

In microstructure modeling, a total of 4 layers and 5 scans for each layer were simulated for each process condition. Figure 8 shows the representative peak temperature contour from parameter set #C in Table 2. This figure represents the peak temperature of each location during the printing process. The other four conditions (#A, #B, #D, #E) show a similar contour but have different magnitudes. The peak temperature increases when increasing laser density from #A to #E. It should be noted that boiling effect is not considered in the simulation, as such, simulated peak temperature might be higher than actual peak temperature. However, this will not impact the qualitative comparison among all conditions. Figure 9 shows the simulated microstructure results. This figure represents grain orientation, which ranges from 0 deg to 90 deg. The black area represents voids. Both lack-of-fusion porosity and keyhole/boiling porosity were modeled.

Comparison of experimental data and simulation results reveals that porosity prediction agrees with experimental results in two aspects: (1) at energy density levels below the optimal value, porosity decreases with increase of energy density; while at energy density levels above the optimal value, it increases with an increase of energy density and (2) voids appear more spherical at high energy density samples (#D and #E) than the low energy density samples (#A and #B).

Also, Fig. 10 shows a quantitative comparison between experiment and simulation. For the predicted porosity level, there is good agreement with experimental results in most cases, except for sample #B which overpredicted the porosity. This is possibly because condition #B is near the transition zone from lack of fusion to fully melted, and the current thermal model is not developed well enough to capture such transition. This thermal model can be improved by calibrating the model coefficients through building more coupon samples.

In this section, DCAM platform validation against two different manufacturing processes, namely, AM and CM (machining), is considered at the coupon level. At the coupon level, a series of 17-4 PH stainless steel dogbone samples were made by both AM and CM processes. Figure 11 shows the dimensions of the dogbone samples used in this section. The manufactured coupons’ material properties and microstructure were analyzed, and then testing was performed to assess their mechanical and fatigue properties. DCAM was used to simulate the microstructure of both AM and CM coupons, and then used to simulate the fatigue performance at different axial loading conditions. Simulation results were validated against experimental fatigue data. A total of 35 AM dogbone coupons were made by a laser powder bed fusion process, and a total of 35 CM dogbone coupons were made by a conventional process. These manufactured dogbone coupons were used for material characterization and testing.

In-depth analysis was performed to obtain the following technical inputs to DCAM:

• – Grain size, morphology, and distribution

• – Case microstructure, core microstructure, case-core transition region microstructure

• – Defects, nonmetallic inclusions size distribution (mean size, variance, density type)

• – Microhardness profile

Figure 12 shows the characterization results of a CM dogbone coupon. Characterization results show that the CM coupon consists of precipitation—hardened martensitic microstructure. Samples are through-hardened with an average microhardness of about 38 HRC. Small metallic inclusions less than <10 µm are observed in the un-etched microstructure. SEM and etched images revealed martensitic microstructure with Cu precipitates within the grains. Small patches within the case microstructure are observed to be decorated by precipitates. Core microstructure contains patches of untransformed martensitic microstructure.

Figure 13 shows characterization results of an AM dogbone coupon. Microhardness measurements on the samples revealed an average hardness of about 40 HRC. AM samples also consisted of martensitic microstructure with the presence of copper precipitates. Cr precipitates are also observed within the martensitic grains. Precursor powder particles separated from the matrix can be seen in the specific areas.

After microstructure characterization, mechanical testing, including tensile and axial fatigue tests, were performed at University of Nevada—Reno (UNR). Fully reversed strain-controlled tension-compression fatigue experiments were conducted on specimens of 17-4 PH stainless steels fabricated by AM and CM. All the experiments were conducted in ambient air. For fatigue experiments, a total of 40 specimens were tested at different loading amplitudes to form S-N fatigue curves. A servohydraulic fatigue testing machine was used for the required fatigue experiments of 17-4 PH stainless steels. In the experiment, a dogbone sample was loaded in the axial direction so that the stress and strain within the gage section of the testing specimen are uniform. The diameter in the gage section of the testing specimen was 8.0 mm and the gage section length was 16.0 mm. The testing frequency ranged from 0.25 Hz for large strain amplitudes (low fatigue life) to 10 Hz for low loading amplitudes (high fatigue life). During the experiment, the strain amplitude was controlled and both the applied axial stress and the strain within the gage section of the testing specimen were measured.

Fatigue life is defined as the number of loading cycles to the total separation of the testing specimen into two pieces. The stress-life (stress amplitude versus fatigue life) curve of the materials is shown in Fig. 14. For a strain-controlled experiment, the stress amplitude was taken at approximately half fatigue life. The fatigue limit of the conventionally manufactured 17-4 PH stainless steel is approximately 640 MPa and the fatigue limit of the additively manufactured stainless steel is approximately 300 MPa.

In summary, the two manufacturing conditions result in similar static strengths but the CM 17-4 PH steel has a significantly higher ductility. The fatigue strength of the CM 17-4 PH steel is higher than its AM counterpart. The fatigue limit of the conventionally manufactured 17-4 PH stainless steel is approximately 640 MPa and the fatigue limit of the additively manufactured stainless steel is approximately 300 MPa. All the fatigued specimens have an identical feature of fracture surface as shown in Fig. 15. The fatigue crack surface is perpendicular to the axis of the testing specimen. For more details on the fatigue testing of these samples please refer to Ref. [34].

Now, DCAM modeling tool is used to predict the durability of AM and CM coupons at different loading conditions. The first step is to perform macro-scale finite element analysis to determine hot spot. Commercial FEA package abaqus was used in this step. In the FEA analysis, the bottom section of dogbone coupon was fixed with no displacement allowed, and the top surface was applied displacement load. As expected, the stress concentration is in the gauge area. Five different stress amplitudes (75 MPa, 125 MPa, 175 MPa, 212.5 MPa, 250 MPa) were selected for fatigue simulation in DCAM.

After completing the macro-level simulation, DCAM is used to simulate the microstructure for both CM and AM dogbone samples. For AM coupon, layer-by-layer manufacturing process is used, as explained in Sec. 2.2. We generated total of 15 2D microstructure domains in the size of 1000 µm × 500 µm. This represents a total of 12 printing layers and ten scans at each layer. Figure 16(a) shows a representation of simulated microstructure of additively manufactured 17-4 PH stainless steel. It should be noted that the total 15 microstructure simulations have the same thermal input, but also lead to variation of grain size and orientation in the final microstructure. For CM coupon, we used Voronoi tessellation modeling technique which is designated for CM materials to generate 15 microstructures. Similarly, those microstructural domains have the same input, while have some variation in grain size and orientation representing the statistical nature. Figure 16(b) shows representative CM microstructure. As seen, there is a clear difference between AM and CM microstructure, which is the primary factor that leads to different mechanical and dynamic properties of final component.

Figures 17 and 18 plot the simulation results for CM and AM dogbone coupons, and comparison with experimental testing. As seen, DCAM tool has a very good agreement with experimental testing for both CM and AM materials. Figure 19 compares the CM and AM simulation results, indicating that CM coupon has a strong fatigue performance than AM coupon, which aligns with experimental results showed in Sec. 3.2.

Four batches of 17-4 PH dogbones (Fig. 20) were printed on a powder bed fusion machine (Lumex Avance). As shown in Fig. 21, Batch 1 used the machine default printing conditions with laser power of 320 W. Batch 2 used reduced laser power, 240 W. Batch 3 used normal laser power but the samples are printed 60 deg inclined (normal printing parameters with an inclination angle to introduce different surface roughness). Batch 4 used a reduced laser power 240 W and a random hatch scanning strategy, which means at each layer, the laser scans island contours at random pattern instead of scanning contours in an ordered pattern.

The porosity was characterized using Archimedes’ principle. Results are shown in Fig. 22. 320 W and 240 W RH have slightly high porosity. The measured porosity of all four batches is lower than 0.6%.

Table 3 shows the surface roughness Ra of the as-build surfaces. Batch 1 and 2 have very similar roughness. The upskin and downskin surfaces of Batch 3 have higher surface roughness. Downskin surface has higher surface roughness than upskin surface as expected because of the overhang effect of downskin surface. Figure 23 shows the morphology of the as-built surfaces. It is observed that many partially unmelt particles are fused to solid structure.

Tension-tension testing was conducted with a stress ratio of 0.1 to avoid buckling since the dogbone samples were very thin. The testing frequency was set at 10 Hz because significant vibration was observed at higher frequencies. The testing results are shown in Fig. 24. 320 W is the machine default laser power, which shows the highest fatigue life. Fatigue life of 240 W is similar to 320 W at 500 MPa and 300 MPa. At 400 MPa, the fatigue life of 240 W is even higher than 320 W. The original plan for the second batch 240 W was to reduce laser power to introduce porosity. However, the microstructure analysis shows 320 W and 240 W has similar porosity levels. At 400 MPa, the 240 W even shows higher fatigue life. Nonetheless, compared with 320 W, 240 W shows higher variability, the fatigue performance is not consistent.

There is not enough data to differentiate the fatigue life between 320 W (Batch 1) and inclined (Batch 3) statistically. Although 320 W 60 deg inclined batch has much higher surface roughness, it is not enough to cause a significant decrease in fatigue life. The 240 W random hatch batch has the lowest fatigue life. In random hatch scanning pattern, after one hatch is scanned, the laser moves to a different location, the material cools down immediately. Comparing with a continuous scan, the random hatch scan has a higher cooling rate, especially at the hatch boundaries. The high cooling rate at the hatch boundary may cause high residual stress and reduce the fatigue life.

In this case study, the effect of surface roughness was incorporated in the grain-level crack initiation and propagation simulations. Surface profiles were generated based on measured surface roughness Ra values. The node coordinates were adjusted so that the top surface of the microstructure domain was consistent with the generated surface profiles. The comparison of experiment and simulation of fatigue life at different process conditions is given in Figs. 25–27. For each condition, the fatigue testing was repeated three times. The simulation for each case was repeated many times with little extra costs, which are the major benefits of simulation. The simulations provide a distribution of fatigue life instead of a single value. The experimental results fall in the range of the simulation results, which indicates that the simulation has good agreement with experiment.

Comparing Figs. 25–27, i.e., comparison between experiment and simulation of different process conditions, the experiment shows that the fatigue life of 320 W and 320 W 60 deg inclined is very close, which is successfully captured in the simulation. Both the experiment and simulations show that 240 W has higher variation than 320 W. Therefore, the fatigue prediction can consider the effect of process parameters, which can be used to optimize process parameters and reduce trial-and-errors in experiment.

Two types of IN718 coupons were built using Lumex Avance 25 laser powder bed fusion machine. The first type is the bridge coupon that is from NIST AM benchmark test series, which is considered a standard geometry for part distortion measurement [35]. Figure 28 shows both coupon geometries. The second type is a cuboid coupon that is used to validate microstructure model. Table 4 lists the process parameters that are used to build those coupons. In order to reduce experimental error, four identical bridge coupons were built using the same conditions, and cuboid coupons were repeated three times for each condition.

Distortion measurements were taken from bridge coupons using the same method illustrated in NIST AM-bench [35]. The height of each ridge (shown in Fig. 29) to the top surface of the build plate was measured after all legs of the bridge were separated from build plate using wire electric discharge machining (wire-EDM), allowing the part to deflect upward due to the residual stress. The measured height was subtracted by original height (12.5 mm based on computer-aided design (CAD)) to represent deflection magnitude. Two measurement techniques (digital image correlation and calipers measurement) were used to increase the measurement accuracy. All four bridge coupons were measured, and results are listed in Fig. 29.

The cuboid coupons were examined regarding grain structure and porosity. After successfully built, those coupons were removed from substrate plate using wire-EDM. Porosity was firstly characterized using image analysis method. Figure 30 shows the representative porosity image under optical microscope. After the porosity measurement, coupon #C2 were examined using EBSD method for grain structure analysis. Figure 31 shows the EBSD image from three different cross sections.

The DCAM tool was applied to simulate the printing process of both bridge and cuboid coupons. Process model was run for bridge coupons to simulate the bridge distortion. After simulation was completed, an extra step was taken to remove finite element from the part bottom to mimic the wire-EDM process in the experiment. Figure 32 shows the displacement contour after certain elements were removed. As seen from the figure, the bridge bent upward that aligned with experimental observation. In addition, microstructure model was run for the cuboid coupons under all three conditions. Figure 33 shows the representative microstructure modeling results from coupon #C2.

Figure 34 shows the comparison of DCAM modeling and experiment regarding part-level distortion. Experimental data points were averaged from all four repeated bridges. As seen from the figure, the distortion prediction in DCAM aligns with experimental results very well. Grain structure modeling results from coupon #C2 were compared with experimental results. Two-dimensional images from different cross sections were consolidated to construct a 3D view as plotted in Fig. 35. As seen from the figure, simulated grain morphology aligned with the experimental results very well. Also, the simulated grain size at each cross section was analyzed and compared with experimental data. The bar chart shows that predicted average grain size agreed with the experimental results very well. In addition, Fig. 36 shows comparison of modeling and experimental results regarding porosity at different laser powers. In the experiment, porosity decreases when laser power increases, and a similar trend was observed in the simulation.

In this section, we present the results of a research work on single gear tooth under root bending fatigue testing. This component was selected based on the request we received from our aerospace OEMs customers. We built gear tooth samples from Ferrium C64 alloy using an electron beam melting machine. Ferrium C64 is one of only a few carburizable steels that has been atomized and processed by AM methods [36]. It can meet the demands for high strength, high toughness, and high thermal resistance required of gears, bearings, and power transmission shafts produced for aerospace and power generation applications.

Please note that for this sample we are using a different AM machine compared with previous samples, i.e., electron beam versus laser sintering. This will add value to our modeling tool through considering more number of additive manufacturing processes. One of the finished gear tooth samples manufactured using electron beam AM machine is shown in Fig. 37. Gear tooth samples were sent to Pennsylvania State University Gear Research Institute for single tooth bending fatigue (STF) testing and to the material lab to perform material characterization on them such that we can use their material properties in our predictive DCAM modeling tool.

Gear tooth samples were characterized near the root surface. Optical microscopy was used to characterize the gear tooth samples. ASM International (American Society of Metals) guidelines were sued to metallographically prepare and characterize the samples. As viewed in Fig. 38, microscopy images of the sample show that the sample contains a lot of defects. Also, Fig. 39 further shows that there are a few defects in the sample, observed under SEM.

Microhardness results are illustrated in Fig. 40 for AM gear tooth sample. Gear consists of case-hardened microstructure and meets microhardness specifications. Case microhardness is above 60 and core is around 50 HRC. Gear tooth is case hardened to a depth of 1100 μm. These hardness values are used to determine the material properties to be used in DCAM simulations.

Another major material characterization on the sample is measuring the subsurface residual stress profile generated by surface finishing work. Figure 41 shows the residual stress profile measured by X-ray diffraction (XRD) technique. The outcome of material characterization are the microstructural features and properties of additive manufacturing C64 gear tooth which will be used in DCAM modeling tool.

We requested the assistance of the Gear Research Institute at Pennsylvania State University to perform STF testing on Ferrium C64 gear tooth samples made by AM. Ideally for the fatigue testing, test data would be presented as applied bending stress versus corresponding life for the AM C-64. Due to the specific geometry of these gear tooth samples, an approximate load to stress factor was computed by assuming the test gear was an 11 DP, 20 deg pressure angle, 0.500 in. face width spur gear with 1000 teeth. The large number of teeth generates a big gear with nearly straight sided teeth to serve as an approximation. The load to bending stress factor was then computed using the Lewis parabola method. The approximate load to bending stress factor is 37.8 psi/pound of applied load. The load point was 0.057 in. from the tip of the tooth which was verified visually on the test parts using layout paint. A total of 23 STF tests were conducted. Test particulars are given in Table 5. Tests were conducted at ambient temperature in room air with 600 W oil applied to the contact point. The run-out limit for this set of tests was set at ten million cycles.

The limiting factor for test frequency is the ability to maintain a satisfactory waveform in the loading, which is controlled by the hydraulic capacity of the test machine. Setup tests showed that this limiting frequency was 45 Hertz. Accordingly, all program tests were conducted at 45 Hertz. Test results are later used to validate our predictive modeling tool. Representative photographs of test specimens after testing are shown in Fig. 42.

Fracture analysis was performed on two broken teeth. A short cycle and moderate/long cycle failure were selected for optical evaluation. Fracture surface images are given in Fig. 43. The failure origin from Test 1 (Tooth 9) was located at the surface on the left side of the fracture face, not at the edge. This is indicative of even loading across the flank and proper fixture alignment. The longer duration Test 4 (Tooth 11) had indications that the fracture origin was at the edge of the tooth. This is not surprising due to the lack of edge break chamfers on these samples. The addition of an edge chamfer would likely extend the lives of the moderate and longer cycle failures.

After fatigue testing of these single gear tooth samples, it can be concluded that the single tooth bending fatigue performance of additively manufactured C-64 exhibited a traditional stress-life relationship in the finite life regime and showed indications that an infinite life regime may exist if surface load initiated failures could be eliminated. In order to increase the fatigue performance of these teeth samples, we can add finish ground and edge chamfer to them. This would serve three purposes. First, it would reduce the presence of primary carbide networks near the surface and reduce the high surface roughness in the dedendum/fillet; both of which can act as fatigue initiation sites. Second, it would likely eliminate the contact point initiated failures by reducing the surface roughness of the “as built” AM surface resulting in lower contact stress at the load point. Lastly, the occurrence of edge origin failures would likely be eliminated through the edge chamfer addition.

First, we perform the macro-level loading FE analysis on AM gear tooth sample. For this purpose using the CAD model for this component, we made the finite element model of gear tooth specimen which is under tooth bending loading in commercial finite element code abaqus. The model is then properly partitioned and meshed. A finite element analysis of global stresses (i.e., bending fatigue loading in this case) acting on the additively manufactured Ferrium C64 gear tooth is conducted. We identify the area of stress concentration based on the FEA results, and then extract the boundary conditions and time-dependent loading for the further analysis in DCAM. Figure 44 shows the stress contour in three directions for this component. As seen, the highest tensile stress for the gear tooth happens at the root of the gear tooth, as expected. This is where we put our RVE and extract its boundary condition to use in DCAM simulation for prediction of fatigue life.

Now that we have gathered the experimental S-N data for AM gear tooth under bending fatigue loading, we can use it to validate our computational DCAM predictions. For this purpose, first we generate Ferrium C64 microstructure RVE domains using DCAM process and microstructure modules. We generate the RVE of the AM gear tooth specimen which has the same RVE dimensions that we used in the macro-level load analysis in order to extract boundary conditions. In order to consider effect of the microstructure randomness, we generate 11 different domains. They all have microstructures statistically similar to C64 samples inspected. However, their microstructure distribution details are different. One of these microstructures is shown in Fig. 45. Multiple built layers and different laser scan paths are clearly observed in the figure, an output of our DCAM modeling tool. It can be seen that the microstructure generated for C64 samples is quite different than the one generated for Ti6-4 before. This is due to the different material properties of these two materials as well as different AM process parameters used on the AM machine to build these samples.

Now, in order to perform DCAM validation, we put all 11 domains generated under the loading conditions extracted from macro level load analysis. It should be noted that these boundary conditions are resulted due to the effect of macro applied loads to the full geometry of the gear tooth. Figure 46 shows the crack growth at the time of final failure for two samples under different applied loads. As seen, the nucleation of the first microcrack happens at the surface due to the stress concentrations on the edge of specimen. After creation of first microcrack, as crack grows cross the width of specimen, there is always local stress concentration at the tip of crack, which helps the crack growth. Figure 46 shows at the end of simulation crack has grown cross the width of domain. At this point, crack has grown long enough that is unstable and cross section of the specimen cannot carry the applied load anymore, therefore, the final static fracture happens resulting in the gear tooth failure. It also can be seen that different microstructure distribution results in different crack patterns.

Figure 47 shows the comparison between the experimentally generated S-N data and DCAM predictions for all samples. As seen, there is a very good agreement between the S-N data for both sets. Once again, considering different microstructure domains in DCAM results in a range of fatigue lives even for a constant load level (similar to any experimental fatigue testing). The good agreement between S-N data generated experimentally and using DCAM tool for C64 gear tooth samples is considered as another validation of our predictive DCAM modeling tool.

In Sec. 3, different examples of application of DCAM framework was provided for different AM materials and type of loadings. However, none of those examples is directly any tribological application. Instead it was intended to demonstrate the feasibility and applicability of an ICME modeling framework for AM parts. Although we have not yet applied DCAM technology to any contact mechanic application, we have used our general DigitalClone (DC) technology to analyze various tribology/contact mechanics projects for traditional (non-AM) materials. Now, in this section one example of application of our DC technology to a tribology problem is demonstrated. For this purpose, we have selected fretting fatigue testing of 4140 steel dogbone samples under fretting contact loading with Titanium 6–4 contact pads.

The 4140 steel dogbone sample specimen and Ti6-4 contact pad are shown in Fig. 48. The size difference between these two parts can be observed. To apply cyclic axial load, the specimen would be clamped on the MTS machine. To perform fretting fatigue test, a custom designed fretting fixture is attached to the test frame. Two contact pads will hold the specimen from both sides. Figure 49 shows how the two contact pads are pressing two faces of tensile specimen, which can be considered like a third grip around the specimen. Due to this, different cyclic load is felt by the specimen above and below the contact area. Therefore, two load cells are needed on either end of the specimen in order to measure these two different tensile loads on both ends of the specimen. The difference between the two loads is the tangential load (Q) transmitted between the contact pads and specimen.

During fretting testing, total of ten fretting fatigue tests were done on the specimens. These tests were all performed under the same contact pressure (2.9–3.0 GPa), but with different axial loads (all with R = −1). One of the tests (test #4) and its results are described in details in this section and only a summary of the results for the rest of tests are shown. Please note that tests are stopped when the specimen is completely broken or crack has propagated through much of the cross section such that the specimen cannot properly carry the applied loading. The general geometry and material parameters for these tests are

• – Type of test: fretting fatigue test

• – Materials: 4140 steel dogbone specimen and Ti 6–4 contact pads

• – Area of cross section of specimen: 0.0992 in.² = 64 mm²

• – Length of specimen between the MTS grips: 7.0866 in. = 180 mm

• – Axial force ratio: R = −1

• – Axial loading frequency: 5 Hz

Fretting zones on both sides of the specimen and final fretting crack are shown in Fig. 50 for one of the dogbone samples after the test was stopped. As seen, the crack started in the fretting zone on the specimen surface and initially growing in a 45 ft angle indicating that the crack was originally initiated due to fretting loading. After initial grow (when the crack has grown outside the area affected by fretting loading), the crack is continuing its propagation through the specimen thickness and perpendicular to the axial loading direction. This confirms that once the crack is far enough from the fretting zone, it is not affected by fretting loading anymore, but it is driven by bulk axial stresses (like classic fatigue). The fatigue results of these 10 tests are later used to validate DC modeling framework. For more details on this fretting fatigue test rig and test results, please refer to Ref. [37].

In this section, validation of DC model for a fretting fatigue application is demonstrated. First, a macro-level load analysis of fretting fatigue test used to generate the experimental data, is performed. Because of symmetry existing in the specimen and loading, the model is cut by symmetry planes x–y and x–z to decrease the computational costs. The desired output from this simulation is the displacements of the nodes on the desired RVE, which acts as an input to the DC model.

Next step is to create the microstructure model. For these simulations, as these samples are a non-AM material, we use DC conventional microstructure generator. This generator uses Voronoi tessellation and microstructure parameters obtained in material characterization to simulate the RVE microstructure. In this approach, RVE is filled with randomly shaped grains simulating the material microstructure of the dogbone specimen. In order to consider the randomness of material microstructure and its effect on the fretting fatigue life, three domains with different granular structure are generated for each load level. One microstructure sample is shown in Fig. 51.

Having the material microstructure, pressure and shear tractions, and boundary conditions, DC model performs the simulation iteratively including the damage accumulation and stress updating resulting in microcrack nucleation, crack propagation, and eventually pit/spall formation. Figure 51 shows the crack growth through the microstructure with continuation of the simulation. As seen, fretting crack initiates on the surface close to the edge of contact zone which is in agreement with the previous findings in the literature. After initiation on the surface, fretting crack keeps growing inward into the contact zone with a 45 deg angle due to fretting loading. This is a significant observation which is along with previous findings for fretting problem in different literatures. Also, as simulation continues and crack propagates, a surface pit forms and grows.

Figure 52 compares the experimental S-N data obtained from fretting fatigue test rig and DC fretting model results. As seen, there is a good agreement between the experimental fretting lives and DC prediction results especially in lower loads range.

In this section, a fretting fatigue testing and simulation were described to demonstrate the feasibility and applicability of our modeling framework for tribological applications. This specific example was selected for a non-AM material because our recently developed DCAM has not yet been applied to any tribological application. However, it should be noted that in order to perform tribological simulation for an AM part, we just need to use AM process and microstructure modules to create the AM microstructure and then the fatigue module will be similar to what was shown in this section for a non-AM material.

The overall purpose of this research is to develop a predictive modeling tool for components built using AM and assess their performance, with rigorous consideration of the microstructural properties governing the nucleation and propagation of fatigue cracks. In this paper, we presented our DCAM modeling framework. We demonstrated the feasibility of developing such a modeling tool and validation using experimental testing. Our predictive model has three main modules: process modeling, microstructure modeling, and fatigue modeling. The process module uses the part geometry and AM process parameters to predict the residual stress and distortion left in the part at the end of build process as well as thermal history of the part. The microstructure module uses these thermal histories and material properties to predict the microstructure of AM part including grain structure and distribution and porosity. The fatigue module utilizes the outcome of the previous modules along with the fatigue loading conditions to predict the failure behavior and fatigue life of the AM part.

DigitalClone for additive manufacturing considers multiple microstructural features specific to AM materials: effect of the AM build process on the residual stress left in the part, surface roughness created on part surface, and microstructure resulted due to build process parameters. AM build parameters (laser intensity, laser speed, hatching space, powder layer thickness, orientation of build, etc.) are considered in our process modeling. In the validation section, we presented the research results on multiple AM coupon samples with different geometries and materials. For all of these parts, the material characterization results were shown. Also, the experimental fatigue results were reviewed to perform the validation of our DCAM modeling tool. It was shown that our predictive modeling tool agrees well with experimental results for both microstructure and performance across multiple geometries, AM materials, and loading conditions. This tool provides a technically effective way for part qualification and product design in metal additive manufacturing across different industries.

To design and qualify an AM component for any tribology application (for example, bearings and gears) the first step is to go through the material characterization and qualify the AM microstructure and process using coupon level testing and validation. For this purpose, DCAM modeling tool and steps shown in this paper are not only relevant, but also necessary to reduce the cost and time of such a qualification process and increase the efficiency and performance of the final product.

The authors express their deepest appreciations to Professor Farshad Sadeghi at Purdue University, Professor Yanyao Jiang at University of Nevada, Reno, Professor Michael Sealy at University of Nebraska-Lincoln, and Mr. Aaron Isaacson at Gear Research Institute at Pennsylvania State University for their contributions on fatigue testing of different coupon samples presented in this paper. Also, the authors express their deepest appreciations to Dr. John Slotwinski at Johns Hopkins University Applied Physics Laboratory for his contribution on manufacturing and material characterization of AlSi10Mg coupon samples.

There are no conflicts of interest.

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request. The authors attest that all data for this study are included in the paper.