Inverse Method to Determine Parameters for Time-Dependent and Cyclic Plastic Material Behavior from Instrumented Indentation Tests.

Indentation is a versatile method to assess the hardness of different materials along with their elastic properties. Recently, powerful approaches have been developed to determine further material properties, like yield strength, ultimate tensile strength, work-hardening rate, and even cyclic plastic properties, by a combination of indentation testing and computer simulations. The basic idea of these approaches is to simulate the indentation with known process parameters and to iteratively optimize the initially unknown material properties until just a minimum error between numerical and experimental results is achieved. In this work, we have developed a protocol for instrumented indentation tests and a procedure for the inverse analysis of the experimental data to obtain material parameters for time-dependent viscoplastic material behavior and kinematic and isotropic work-hardening. We assume the elastic material properties and the initial yield strength to be known because these values can be determined independently from indentation tests. Two optimization strategies were performed and compared for identification of the material parameters. The new inverse method for spherical indentation has been successfully applied to martensitic steel.

Optimizing Fatigue Performance in Gradient Structural Steels by Manipulating the Grain Size Gradient Rate.

As a new type of high-performance material, gradient structural steel is widely used in engineering fields due to its unique microstructure and excellent mechanical properties. For the prevalent fatigue failure problem, the rate of change in the local grain size gradients along the structure (referred to as the gradient rate) is a key parameter in the design of gradient structures, which significantly affects the fatigue performance of gradient structural steel. In this study, a new method of 'Voronoi primary + secondary modeling' is adopted to successfully establish three typical high-strength steel models corresponding to the convex-, linear-, and concave-type gradient rates for gradient structures, focusing on the stress-strain response and crack propagation in structural steel with different gradient rates under cyclic loading. It was found that the concave gradient rate structural model is dominated by finer grains with larger volume fraction, which is conducive to hindering fatigue crack propagation and has the longest fatigue life, which is 16.16% longer than that of the linear gradient rate structure and 23.66% longer than that of the convex gradient rate structure. The simulation results in this study are consistent with the relevant experimental phenomena. Therefore, when regulating the gradient rate, priority should be given to increasing the volume fraction of fine grains and designing a gradient rate structure dominated by fine grains to improve the fatigue life of the material. This study presents a new strategy for designing engineering materials with better service performance.

Mechanical Behavior of Austenitic Steel under Multi-Axial Cyclic Loading.

Low-nickel austenitic steel is subjected to high-pressure torsion fatigue (HPTF) loading, where a constant axial compression is overlaid with a cyclic torsion. The focus of this work lies on investigating whether isotropic J2 plasticity or crystal plasticity can describe the mechanical behavior during HPTF loading, particularly focusing on the axial creep deformation seen in the experiment. The results indicate that a J2 plasticity model with an associated flow rule fails to describe the axial creep behavior. In contrast, a micromechanical model based on an empirical crystal plasticity law with kinematic hardening described by the Ohno-Wang rule can match the HPTF experiments quite accurately. Hence, our results confirm the versatility of crystal plasticity in combination with microstructural models to describe the mechanical behavior of materials under reversing multiaxial loading situations.

Micromechanical Modeling of AlSi10Mg Processed by Laser-Based Additive Manufacturing: From as-Built to Heat-Treated Microstructures.

The unique microstructure of the alloy AlSi10Mg produced by the laser-based powder bed fusion of metals (PBF-LB/M) provides high-strength and high-strain-hardening capabilities of the material. The microstructure and mechanical properties of 3D-printed, i.e., additively manufactured, AlSi10Mg are significantly altered by post-building heat-treatment processes applied in order to tailor the final properties of the parts. Using an accurate computational model to predict and improve the mechanical performance of 3D-printed samples considering their microstructural features can accelerate their employment in envisaged applications. The present study aims to investigate the correlation between microstructural features and the mechanical behavior of as-built, direct-aged, and T6 heat-treated samples of PBF-LB/M AlSi10Mg under tensile loading using experiment and microstructure-sensitive modeling approaches. Nanoindentation tests are used to calibrate the parameters of the constitutive models for the Al and Si-rich phases. The experimental investigations revealed that heat treatment significantly changes the sub-grain morphology of the Si-rich phase, and this can have a considerable effect on the mechanical behavior of the components. The effect of the modeling of the Si-rich phase in the representative volume elements on the prediction of mechanical behavior is investigated using the J2 plasticity model. The combination of the crystal plasticity model for Al and the J2 plasticity model for the Si-rich phase is used to predict the tensile properties of the as-built and heat-treated states. The predicted results are in good agreement with the experimental results. This approach can be used to understand the microstructure-property relationship of PBF-LB/M AlSi10Mg and eventually tailor heat treatment for PBF-LB/M AlSi10Mg based on the requirement of the application.

Influence of Temperature on Void Collapse in Single Crystal Nickel under Hydrostatic Compression.

Employing atomistic simulations, we investigated the void collapse mechanisms in single crystal Ni during hydrostatic compression and explored how the atomistic mechanisms of void collapse are influenced by temperature. Our results suggest that the emission and associated mutual interactions of dislocation loops around the void is the primary mechanism of void collapse, irrespective of the temperature. The rate of void collapse is almost insensitive to the temperature, and the process is not thermally activated until a high temperature (∼1200-1500 K) is reached. Our simulations reveal that, at elevated temperatures, dislocation motion is assisted by vacancy diffusion and consequently the void is observed to collapse continuously without showing appreciable strain hardening around it. In contrast, at low and ambient temperatures (1 and 300 K), void collapse is delayed after an initial stage of closure due to significant strain hardening around the void. Furthermore, we observe that the dislocation network produced during void collapse remains the sample even after complete void collapse, as was observed in a recent experiment of nickel-base superalloy after hot isostatic pressing.

Data-Oriented Constitutive Modeling of Plasticity in Metals.

Constitutive models for plastic deformation of metals are typically based on flow rules determining the transition from elastic to plastic response of a material as function of the applied mechanical load. These flow rules are commonly formulated as a yield function, based on the equivalent stress and the yield strength of the material, and its derivatives. In this work, a novel mathematical formulation is developed that allows the efficient use of machine learning algorithms describing the elastic-plastic deformation of a solid under arbitrary mechanical loads and that can replace the standard yield functions with more flexible algorithms. By exploiting basic physical principles of elastic-plastic deformation, the dimensionality of the problem is reduced without loss of generality. The data-oriented approach inherently offers a great flexibility to handle different kinds of material anisotropy without the need for explicitly calculating a large number of model parameters. The applicability of this formulation in finite element analysis is demonstrated, and the results are compared to formulations based on Hill-like anisotropic plasticity as reference model. In future applications, the machine learning algorithm can be trained by hybrid experimental and numerical data, as for example obtained from fundamental micromechanical simulations based on crystal plasticity models. In this way, data-oriented constitutive modeling will also provide a new way to homogenize numerical results in a scale-bridging approach.

Elucidating the dual role of grain boundaries as dislocation sources and obstacles and its impact on toughness and brittle-to-ductile transition.

In this paper, we resolve the role of grain boundaries on toughness and the brittle-to-ductile transition. On the one hand, grain boundaries are obstacles for dislocation glide. On the other hand, the intersection points of grain boundaries with the crack front are assumed to be preferred dislocation nucleation sites. Here, we will show that the single contributions of grain boundaries (obstacles vs. source) on toughness and the brittle-to-ductile transition are contradicting, and we will weight the single contributions by performing carefully designed numerical experiments by means of two-dimensional discrete dislocation dynamics modelling. In our parameter studies, we vary the following parameters: (i) the mean free path for dislocation glide, δ, combined with (ii) the (obstacle) force of the grain boundary, ϕ, and (iii) the dislocation source spacing along the crack front, λ. Our results show that for materials or microstructures for which the mean distance of the intersection points of grain boundaries with the crack front is the relevant measure for λ, a decrease of grain size results in an increase of toughness. The positive impact of grain boundaries outweighs the negative consequences of dislocation blocking. Furthermore, our results explain the evolving anisotropy of toughness in cold-worked metals and give further insight into the question of why the grain-size-dependent fracture toughness passes through a minimum (and the brittle-to-ductile transition temperature passes through a maximum) at an intermediate grain size. Finally, a relation of the grain-size-dependence of fracture toughness in the form of K(dδ, dλ) = KIC + kdδ0.5/dλ is deduced.

Robust Optimization Scheme for Inverse Method for Crystal Plasticity Model Parametrization.

A bottom-up material modeling based on a nonlocal crystal plasticity model requires information of a large set of physical and phenomenological parameters. Because of the many material parameters, it is inherently difficult to determine the nonlocal crystal plasticity parameters. Therefore, a robust method is proposed to parameterize the nonlocal crystal plasticity model of a body-centered cubic (BCC) material by combining a nanoindentation test and inverse analysis. Nanoindentation tests returned the load-displacement curve and surface imprint of the considered sample. The inverse analysis is developed based on trust-region-reflective algorithm, which is the most robust optimization algorithm for the considered non-convex problem. The discrepancy function is defined to minimize both the load-displacement curves and the surface topologies of the considered material under applying varied indentation forces obtained from numerical models and experimental output. The numerical model results based on the identified material properties show good agreement with the experimental output. Finally, a sensitivity analysis performed changing the nonlocal crystal plasticity parameters in a predefined range emphasized that the geometrical factor has the most significant influence on the load-displacement curve and surface imprint parameters.

Optimized reconstruction of the crystallographic orientation density function based on a reduced set of orientations.

Crystallographic textures, as they develop for example during cold forming, can have a significant influence on the mechanical properties of metals, such as plastic anisotropy. Textures are typically characterized by a non-uniform distribution of crystallographic orientations that can be measured by diffraction experiments like electron backscatter diffraction (EBSD). Such experimental data usually contain a large number of data points, which must be significantly reduced to be used for numerical modeling. However, the challenge in such data reduction is to preserve the important characteristics of the experimental data, while reducing the volume and preserving the computational efficiency of the numerical model. For example, in micromechanical modeling, representative volume elements (RVEs) of the real microstructure are generated and the mechanical properties of these RVEs are studied by the crystal plasticity finite element method. In this work, a new method is developed for extracting a reduced set of orientations from EBSD data containing a large number of orientations. This approach is based on the established integer approximation method and it minimizes its shortcomings. Furthermore, the L 1 norm is applied as an error function; this is commonly used in texture analysis for quantitative assessment of the degree of approximation and can be used to control the convergence behavior. The method is tested on four experimental data sets to demonstrate its capabilities. This new method for the purposeful reduction of a set of orientations into equally weighted orientations is not only suitable for numerical simulation but also shows improvement in results in comparison with other available methods.

Hydrogen Embrittlement at Cleavage Planes and Grain Boundaries in Bcc Iron-Revisiting the First-Principles Cohesive Zone Model.

Hydrogen embrittlement, which severely affects structural materials such as steel, comprises several mechanisms at the atomic level. One of them is hydrogen enhanced decohesion (HEDE), the phenomenon of H accumulation between cleavage planes, where it reduces the interplanar cohesion. Grain boundaries are expected to play a significant role for HEDE, since they act as trapping sites for hydrogen. To elucidate this mechanism, we present the results of first-principles studies of the H effect on the cohesive strength of α-Fe single crystal (001) and (111) cleavage planes, as well as on the Σ5(310)[001] and Σ3(112)[11¯0] symmetrical tilt grain boundaries. The calculated results show that, within the studied range of concentrations, the single crystal cleavage planes are much more sensitive to a change in H concentration than the grain boundaries. Since there are two main types of procedures to perform ab initio tensile tests, different in whether or not to allow the relaxation of atomic positions, which can affect the quantitative and qualitative results, these methods are revisited to determine their effect on the predicted cohesive strength of segregated interfaces.

Inverse Method to Determine Fatigue Properties of Materials by Combining Cyclic Indentation and Numerical Simulation.

The application of instrumented indentation to assess material properties like Young's modulus and microhardness has become a standard method. In recent developments, indentation experiments and simulations have been combined to inverse methods, from which further material parameters such as yield strength, work hardening rate, and tensile strength can be determined. In this work, an inverse method is introduced by which material parameters for cyclic plasticity, i.e., kinematic hardening parameters, can be determined. To accomplish this, cyclic Vickers indentation experiments are combined with finite element simulations of the indentation with unknown material properties, which are then determined by inverse analysis. To validate the proposed method, these parameters are subsequently applied to predict the uniaxial stress-strain response of a material with success. The method has been validated successfully for a quenched and tempered martensitic steel and for technically pure copper, where an excellent agreement between measured and predicted cyclic stress-strain curves has been achieved. Hence, the proposed inverse method based on cyclic nanoindentation, as a quasi-nondestructive method, could complement or even substitute the resource-intensive conventional fatigue testing in the future for some applications.

Studying Grain Boundary Strengthening by Dislocation-Based Strain Gradient Crystal Plasticity Coupled with a Multi-Phase-Field Model.

One ambitious objective of Integrated Computational Materials Engineering (ICME) is to shorten the materials development cycle by using computational materials simulation techniques at different length scales. In this regard, the most important aspects are the prediction of the microstructural evolution during material processing and the understanding of the contributions of microstructural features to the mechanical response of the materials. One possible solution to such a challenge is to apply the Phase Field (PF) method because it can predict the microstructural evolution under the influence of different internal or external stimuli, including deformation. To accomplish this, it is necessary to take into account plasticity or, specifically, non-homogeneous plastic deformation, which is particularly important for investigating the size effects in materials emerging at the micron length scale. In this work, we present quasi-2D simulations of plastic deformation in a face centred cubic system using a finite strain formulation. Our model consists of dislocation-based strain gradient crystal plasticity implemented into a PF code. We apply this model to study the influence of grain size on the mechanical behavior of polycrystals, which includes dislocation storage and annihilation. Furthermore, the initial state of the material before deformation is also considered. The results show that a dislocation-based strain gradient crystal plasticity model can capture the Hall-Petch effect in many aspects. The model reproduced the correct functional dependence of the flow stress of the polycrystal on grain size without assigning any special properties to the grain boundaries. However, the predicted Hall-Petch coefficients are significantly smaller than those found typically in experiments. In any case, we found a good qualitative agreement between our findings and experimental results.

Modelling Cyclic Behaviour of Martensitic Steel with J2 Plasticity and Crystal Plasticity.

In order to capture the stress-strain response of metallic materials under cyclic loading, it is necessary to consider the cyclic hardening behaviour in the constitutive model. Among different cyclic hardening approaches available in the literature, the Chaboche model proves to be very efficient and convenient to model the kinematic hardening and ratcheting behaviour of materials observed during cyclic loading. The purpose of this study is to determine the material parameters of the Chaboche kinematic hardening material model by using isotropic J2 plasticity and micromechanical crystal plasticity (CP) models as constitutive rules in finite element modelling. As model material, we chose a martensitic steel with a very fine microstructure. Thus, it is possible to compare the quality of description between the simpler J2 plasticity and more complex micromechanical material models. The quality of the results is rated based on the quantitative comparison between experimental and numerical stress-strain hysteresis curves for a rather wide range of loading amplitudes. It is seen that the ratcheting effect is captured well by both approaches. Furthermore, the results show that concerning macroscopic properties, J2 plasticity and CP are equally suited to describe cyclic plasticity. However, J2 plasticity is computationally less expensive whereas CP finite element analysis provides insight into local stresses and plastic strains on the microstructural length scale. With this study, we show that a consistent material description on the microstructural and the macroscopic scale is possible, which will enable future scale-bridging applications, by combining both constitutive rules within one single finite element model.

Micromechanical Modelling of the Influence of Strain Ratio on Fatigue Crack Initiation in a Martensitic Steel-A Comparison of Different Fatigue Indicator Parameters.

Micromechanical fatigue lifetime predictions, in particular for the high cycle fatigue regime, require an appropriate modelling of mean stress effects in order to account for lifetime reducing positive mean stresses. Focus of this micromechanical study is the comparison of three selected fatigue indicator parameters (FIPs), with respect to their applicability to different total strain ratios. In this work, investigations are performed on the modelling and prediction of the fatigue crack initiation life of the martensitic high-strength steel SAE 4150 for two different total strain ratios. First, multiple martensitic statistical volume elements (SVEs) are generated by multiscale Voronoi tessellations. Micromechanical fatigue simulations are then performed on these SVEs by means of a crystal plasticity model to obtain microstructure dependent fatigue responses. In order to account for the material specific fatigue damage zone, a non-local homogenisation scheme for the FIPs is introduced for lath martensitic microstructures. The numerical results of the different non-local FIPs are compared with experimental fatigue crack initiation results for two different total strain ratios. It is concluded that the multiaxial fatigue criteria proposed by Fatemi-Socie is superior for predicting fatigue crack initiation life to the energy dissipation criteria and the accumulated plastic slip criteria for the investigated total strain ratios.

Topic Review: Application of Raman Spectroscopy Characterization in Micro/Nano-Machining.

The defects and subsurface damages induced by crystal growth and micro/nano-machining have a significant impact on the functional performance of machined products. Raman spectroscopy is an efficient, powerful, and non-destructive testing method to characterize these defects and subsurface damages. This paper aims to review the fundamentals and applications of Raman spectroscopy on the characterization of defects and subsurface damages in micro/nano-machining. Firstly, the principle and several critical parameters (such as penetration depth, laser spot size, and so on) involved in the Raman characterization are introduced. Then, the mechanism of Raman spectroscopy for detection of defects and subsurface damages is discussed. The Raman spectroscopy characterization of semiconductor materials' stacking faults, phase transformation, and residual stress in micro/nano-machining is discussed in detail. Identification and characterization of phase transformation and stacking faults for Si and SiC is feasible using the information of new Raman bands. Based on the Raman band position shift and Raman intensity ratio, Raman spectroscopy can be used to quantitatively calculate the residual stress and the thickness of the subsurface damage layer of semiconductor materials. The Tip-Enhanced Raman Spectroscopy (TERS) technique is helpful to dramatically enhance the Raman scattering signal at weak damages and it is considered as a promising research field.

In situ TEM observation of rebonding on fractured silicon carbide.

Silicon carbide (SiC) is widely used in harsh environments and under extreme conditions, including at high-power, high-temperature, high-current, high-voltage and high-frequency. The rebonding and self-matching of stack faults (SFs) is highly desirable to avoid catastrophic failure for SiC devices, especially for specific applications in the aerospace and nuclear power industries. In this study, a novel approach was developed using an eyebrow hair to pick up and transfer nanowires (NWs), in order to obtain in situ transmission electron microscope (TEM) images of the rebonding and self-matching of SFs at atomic resolution. During rebonding and healing, the electron beam was shut off. Rebonding on the fractured surfaces of monocrystalline and amorphous SiC NWs was observed by in situ TEM at room temperature. The fracture strength was 1.7 GPa after crack-healing, restoring 12.9% of that of a single crystal NW. Partial recrystallization along the <111> orientation and the self-matching of SFs are responsible for the rebonding of the monocrystalline NW. In comparison, the fracture strengths were 6.7 and 5.5 GPa for the first and second rebonding, respectively recovering 67% and 55% of that of an amorphous NW. Atomic diffusion contributed enormously to the rebonding on fractured surfaces of an amorphous NW, resulting in a healed surface consisting of an amorphous phase and crystallites. This rebonding function provides new insight into the fabrication of high-performance SiC devices for the aerospace, optoelectronic and semiconductor industries.

Microstructure Design of Tempered Martensite by Atomistically Informed Full-Field Simulation: From Quenching to Fracture.

Martensitic steels form a material class with a versatile range of properties that can be selected by varying the processing chain. In order to study and design the desired processing with the minimal experimental effort, modeling tools are required. In this work, a full processing cycle from quenching over tempering to mechanical testing is simulated with a single modeling framework that combines the features of the phase-field method and a coupled chemo-mechanical approach. In order to perform the mechanical testing, the mechanical part is extended to the large deformations case and coupled to crystal plasticity and a linear damage model. The quenching process is governed by the austenite-martensite transformation. In the tempering step, carbon segregation to the grain boundaries and the resulting cementite formation occur. During mechanical testing, the obtained material sample undergoes a large deformation that leads to local failure. The initial formation of the damage zones is observed to happen next to the carbides, while the final damage morphology follows the martensite microstructure. This multi-scale approach can be applied to design optimal microstructures dependent on processing and materials composition.

Mechanisms of crazing in glassy polymers revealed by molecular dynamics simulations.

Mechanisms leading to initiation of crazing type failure in a glassy polymer are not clearly understood. This is mainly due to the difficulty in characterizing the stress state and polymer configuration sufficiently locally at the craze initiation site. Using molecular dynamics simulations, we have now been able to access this information and have shown that the local heterogeneous deformation leads to craze initiation in glassy polymers. We found that zones of high plastic activity are constrained by their neighborhood and become unstable, initiating crazing from these sites. Furthermore, based on the constant flow stresses observed in the unstable zones, we conclude that microcavitation is the essential local deformation mode to trigger crazing in glassy polymers. Our results demonstrate the basic difference in the local deformation mode as well as the conditions that lead to either shear-yielding or crazing type failures in glassy polymers. We anticipate our paper to help in devising a new criterion for craze initiation that not only considers the stress state, but also considers local deformation heterogeneities that form the necessary condition for crazing in glassy polymers.