Residual stress modeling considering microstructure evolution in metal additive manufacturing
Introduction
In the past several years, metal additive manufacturing (AM) has become a revolutionary technology to build three-dimensional complex parts via metallic powders [1]. The AM parts have various applications in industries such as aerospace, automobile, and medical since many kinds of components and assemblies can be produced using various material systems [2,3]. Parts built via AM have several advantages over conventional manufacturing including, lower density induced lower energy usage, elimination of multi-step manufacturing of intricated parts, no need of specific tools, reduction in material scrap rate, and many more [4,5]. Aside from these advantages, there are still some limitations that impede the applicability of the AM such as steep temperature gradient, residual stress, distortion, anisotropy and heterogeneity in microstructure and mechanical properties [3,6].
During additive manufacturing (AM) processing cycle, parts are subjected to hot deformation and rapid solidification, during which dynamic recrystallization (DRx) often takes place [7]. Through this process, nucleation of new strain-free grains occurs, and these grains grow at the expense of regions full of dislocations. The yield strength of the alloys is largely determined by the size of nucleated grains. In addition to mechanical properties, the initial grain size also affects microstructure evolution of the DRx process. During DRx, grain boundaries are preferred sites for nucleation, so a larger initial grain size provides fewer nucleation site, thus the recrystallization kinetics is slower [8].
Due to the high-temperature gradient in AM, parts usually experience high thermal stress. The thermal stress induce recrystallization which then affects the grain size of the additively manufactured part [9]. At elevated temperature, the augmented grain size reduces the flow stress which changes the yield surface and has a crucial influence on residual stress [10]. Residual stress has an impact on fatigue life of the component, corrosion resistance, crack initiation and growth, and also microstructure and mechanical properties of the materials [11,12]. Marty et al. [13] predicted the recrystallized volume fraction by assuming the spherical grains based on dislocation density . During recrystallization the obtained grain size is equal to , where is the initial grain size and represents the recrystallized volume fraction. Mederious et al. [14] proposed a model to predict the grain size ( in metadynamic recrystallization (MDRx) where they have argued that the standard Zenner-Hollman (Z) parameter could not be used for the corrolation of the grain size variation due to the strong thermal effects during cooling after hot deformation of IN718. They described a new equation as , where c, p, and R are constants, Q represents the activation energy for MDRx, and T is the temperature. For a part produced via AM process to be used in a mission-critical application, a high degree of confidence is required in its quality. A crucial piece of such a qualification is the ability to accurately determine the stress state within the AM part [15]. Different approaches such as experimentation, numerical modeling, and analytical modeling are employed by researchers to determine the residual stress build-up in this process.
Experimental techniques to measure residual stress can be categorized into destructive and non-destructive methods [16]. X-ray and neutron diffractions are the two commonly used techniques for near-surface and volumetric residual stress measurements, respectively. Hole drilling, sectioning, crack compliance are the sub-categories of destructive methods [17]. Strantza et al. [18] measured the residual strains within the Ti-6Al-4 V parts built via laser powder bed fusion (L-PBF) process. They have used X-ray diffraction to determine the strain pattern within the built part. Wu et al. [12] used neutron diffraction method to measure the volumetric residual stress within the 316 L Stainless Steel L-shape bar. The results showed that the residual stress near the middle of the sample tends to be compressive and tensile near surfaces. Heigel et al. [19] utilized the neutron diffraction method to measure the residual stress within the cylindrical parts build via PBF. They concluded that the outer material was in tension, and inner material was in compression. Robinson et al. [20] proposed a new technique to measure the residual stress profile in metal AM. They have investigated the combination of the deflection-based method as well as the contour and hole drilling methods. They have concluded that the residual stress in the parts built via selective laser melting (SLM) manufactured with unidirectional scan strategy is primarily oriented in the scan direction, and the residual stress perpendicular to scan direction is approximately half of that in the scan direction.
Numerical modeling is employed by researchers to predict the residual stress within the AM parts. Ahmad et al. [21] predicted the residual stress in the SLM of Ti-6Al-4 V and IN718 using inherent-strain-based method. They have used contour method to experimentally validate the numerical model. They have concluded that in both material systems the residual stress is highly tensile near the surface and along the edges, and compressive at the center region of the samples. They also concluded that the high tensile residual stress is observed along the build direction. Zhao et al. [22] developed a numerical model to simulate heat transfer and residual stress distribution in direct metal laser sintering (DMLS). They indicated that based on the simulations, the melting and solidification happens at about 1 ms. Moreover, the obtained horizontal normal residual stresses are the dominant stress component compared to vertical normal stress and shear stress. Li et al. [23] gave an overview of residual stress in metal AM. They expressed that the residual stress formation in metal AM is mostly caused by steep temperature gradient and high cooling rate. They also indicated that the magnitude and behavior of the residual stress could be mitigated through in-process methods such as preheating, process planning, and feedback control and post-process methods such as machining and heat treatment.
Although experimental measurements of stresses within the part play a crucial role in the understanding of this phenomenon, experimental measurement of the entire part is challenging and expensive. Finite element modeling (FEM) is also used by many researchers [24]; however, the simulation of the entire process could not be achieved in a traceable amount of time. Consequently, many simplifications in modeling should be undertaken. Moreover, the inverse analysis to optimize the process parameters to achieve the desired part performance cannot be achieved via FEM in a reasonable amount of time [[25], [26], [27]]. In contrast, analytical models validated by physical experiments provide a means to effectively understand, control and optimize the process parameters by allowing for in-situ analysis.
All in all, to the best of our knowledge there is no work on literature to consider the effect of microstructure on residual stress during metal AM. In this work, a physics-based analytical model is proposed to predict the residual stress under DRx effect. A transient moving point heat source approach is used to predict the temperature field by considering the scan strategies of hatching space, layer thickness, and scan path, temperature-dependent material properties, and energy needed for solid-state phase change. As a result of the high-temperature gradient in this process, parts experience thermal stress. The thermal stress build-up in this process is calculated by combining three sources of stresses known as stress due to body force, normal tension, and hydrostatic stress. Thermal stress may exceed the yield strength of the part. As a result, the Johnson-Cook flow stress model is used to predict the yield surface. In this flow stress model, the initial yield strength is related to grain size using Hall-Petch equation. The grain size is calculated using JMAK and grain refinement models during heating and cooling cycles, respectively. As a result of repeated heating and cooling and the fact that the material is yielded, the residual stress is predicted from incremental plasticity and kinematic hardening behavior of the metal according to the property of volume invariance in plastic deformation in coupling with equilibrium and compatibility conditions [28]. The predicted residual stress from the proposed analytical model showed good agreement with X-ray diffraction measurements used to determine the residual stress in IN718 specimens fabricated via DMD process.
In this study the IN718 is used as a material example to validate the proposed analytical mechanics modeling. IN 718 has been widely used is aerospace industries due to its good mechanical properties and structural stability at elevated temperatures.
The mechanical attributes of the fabricated samples highly depend on the grain size, and size, morphology and content of different phases. The phases present in the IN718 samples fabricated via DMD process is evaluated using X-ray diffraction. The results show the existence of phase in all three fabricated samples. It should be note that although the effect of phases on residual stress is not considered, the obtained error is less than 21 % which shows that the proposed model is an effective tool for the prediction of residual stress distribution in an additively manufactured component.
Section snippets
Process modeling
A fully coupled thermomechanical analytical model is proposed to predict the residual stress considering the microstructure of the built part. The high computational efficiency of the proposed model (prediction of residual stress in 2.8 min using a 2.3 GHz Intel Core i5 laptop) makes it a great tool for the optimization of the process parameters and control of the AM process in achieving high-quality components. This section goes into more detail regarding the specific thermal and mechanical
Experimental procedure
Three blocks of IN718 specimens with the size of 10 mm (length) 20 mm (height) 3 mm (width) are manufactured via DMD process using LENS CS 1500 SYSTEMS with the laser wavelength of 1070 nm, under different process conditions as listed in Table 3. Density of the additively manufactured part has a substantial influence on mechanical properties of the fabricated part. Based on the given machine and powder size parameters, an approach to identify processing parameters for producing high-density
Results
In this section, we discuss the results obtained from fully coupled analytical modeling. First, for the selected process parameters, the temperature distribution is obtained. High temperature gradient in this process induced thermal stress. The thermal stress alters the grain size of the build, affected yield strength. The grain size is obtained from dynamic recrystallization and grain refinement models. The relationship between the grain size and yield strength are obtained using Hall-Petch
Discussion
A comparison is conducted to demonstrate the effect of considering microstructure on residual stress prediction. As shown in Fig. 10, Fig. 11, Fig. 12, the residual stress predicted under microstructure effect is compared to the predicted residual stress without considering the microstructure. The predicted residual stress in both cases showed good agreement with the experimental measurements. However, when the effect of microstructure is not considered in the modeling of residual stress, the
Sensitivity analysis
A sensitivity analysis is conducted to investigate the effect of process parameters of laser power and scan speed on residual stress considering the effect of microstructure evolution in additive manufacturing of IN718. The laser power varies from 150 W to 350 W, and the scan speed varies from 300 mm/s to 1000 mm/s. The other parameters including hatching space (105 , layer thickness (250 , and scan path (bi-directional) are kept the same for all the cases. The average through-height
Conclusion
A thermomechanical analytical model is proposed to predict the residual stress considering the effect of microstructure. Thermal loading during metal additive manufacturing process alters the grain size affected yield strength. The grain size is obtained using dynamic recrystallization and grain refinement models. The relationship between the grain size and yield strength are obtained using Hall-Petch equation. Due to the high strain, strain rate, and temperature during metal AM, the
Future work
Due to the impact of texture on material properties of an alloy, authors aim to use their previous work on texture prediction in the additively manufactured part to draw a relationship between texture and residual stress. Moreover, the authors currently working on to improve the model to capture the effect of geometry by considering the effect of heat transfer boundary conditions on the edges of the sample.
Declaration of Competing Interest
The authors report no declarations of interest.
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