Strain-hardening Model Research Articles

Numerical design and experimental validation of shockless plate impact configurations for the Lagrangian analysis of armor ceramics

Ceramic materials are widely used in armor or protective structures, providing weight saving at equivalent performance in comparison to their steel counterparts. Plate-impact experiments are commonly used to investigate the dynamic behavior of ceramics under compressive loading. Using the particle velocity measured at the back of the target, some mechanical properties such as the Hugoniot elastic limit (HEL) as well as the Hugoniot curve of the material can be deduced. Nevertheless, these tests do not provide a direct measurement of the plastic hardening (post-HEL) behavior of the target. In the present work, an experimental shockless plate-impact configuration was developed and implemented to conduct a Lagrangian analysis. This configuration relies on the use of a wavy-machined flyer plate impacting a target made of a buffer, two ceramic plates of different thicknesses, and two window plates as backing. First, the use of wavy flyer plates to generate a loading ramp was validated by considering the impact of the wavy-machined flyer plate against a target, both made of 316L steel. A numerical analysis of this test was developed to confirm the pulse-shaping effect observed experimentally. Next, a ceramic, F99.7 alumina was subjected to the shockless plate impact test in Lagrangian configuration considering the same steel as a buffer and flyer plate material. These tests coupled with Lagrangian analysis enable the curve of axial-stress vs axial-strain beyond the isentropic elastic limit (IEL) to be deduced. The experimental data allow identifying the parameters of an elastoplastic with strain-hardening model to describe the behavior of the tested alumina.

Revealing and predicting the mechanical and strain hardening behaviors of Cu-Al alloys based on microscopic mechanism

In order to reveal and predict the strain hardening behaviors of metallic materials, mechanical properties of Cu-Al alloys processed by rolling were investigated by tensile tests. The microstructure evolution of Cu-Al alloys processed by rolling were characterized. The true stress-strain curves were fitted by an exponential strain-hardening (ESH) model. Based on the microscopic mechanism of dislocation growth and annihilation, the true stress strain curves were predicted through macroscopic mechanical properties. The strengthening effects on Cu-Al alloys of different methods were analyzed quantitively by hardening exponent z and saturation strength σs which were derived from the ESH model. The fundamental assumptions and physical meaning of parameters have been validated by investigating strain hardening behaviors of Cu-Al alloys. The limited applicable materials and future research of ESH model are also proposed for the further development. This study could provide guidance to understand work-hardening behavior and predict tensile performance of Cu-Al alloys.

Nanocarbon architecture-dependent strengthening and deformation in Al matrix composites

The extraordinary strength of inner graphene walls in carbon nanotube (CNT) is barely exerted due to the weak inner-wall shear resistance, which extremely limits its load-bearing capability. To overcome such deficiency, nanocarbon architecture engineering from CNT to graphene nanoribbon (GNR) was performed via longitudinal unzipping of multi-walled CNT, which was utilized to reinforce pure Al. Results show that the activation volume of composites at macroyielding point, evaluated by stress relaxation experiments, monotonically decreases from CNT/Al to GNR/Al, which results in the continuous increase of critical resolved shear stress (CRSS) called for dislocation nucleation/cross-slip at the grain boundaries. Shear-lag model and numerical simulations demonstrate the increased load-transfer effect from CNT/Al to GNR/Al. Meanwhile, the isotropic and kinematic hardening in nanocarbon/Al composites were investigated both by loading-unloading-reloading tests and strain hardening model on basis of dislocation behavior, wherein the effective stress was determined as being larger than back stress in the composites. Detailed analysis further indicates that the nanocarbon architecture from CNT to GNR increases the back stress strengthening due to the enhanced dislocation accumulation at nanocarbon/Al interface. Moreover, as CNT was unfolded to GNR, the failure mode of reinforcements in the composites gradually changed from pull-out to breakage.

Modeling and Crystal Plasticity Analysis of Strain Hardening in Metallic Materials under the Influence of Microstructure

Modeling and Crystal Plasticity Analysis of Strain Hardening in Metallic Materials under the Influence of Microstructure

Residual Stress Analysis of Re-autofrettage of a Swage-Autofrettaged Tube by Computer Modeling Incorporating Accurate Material Representation

Autofrettage processes allow engineers to reduce the thickness of thick-walled cylinders or components in high-pressure applications without sacrificing strength, life, or safety. However, during the autofrettage process, residual stresses will be generated due to plastic deformation. The complex tube material behavior is dominated by the Bauschinger effect. A better understanding and accurate prediction of the residual stress field is critical, which will enable better piping design strategies to minimize deformation and stresses under operating conditions. This study aims to predict and analyze residual stresses resulting from hydraulic re-autofrettage of a swage-autofrettaged thick-walled cylinder by computer modeling. A case study was performed on a thick-walled cylinder of A723 alloy with a radial interference of 2.5%. In order to investigate the effect of the chosen material constitutive representation, results based on the true material constitutive model were compared with the simplified prevalent material model of bi-linear kinematic strain hardening. Computer implementation for the true material was via a user-developed subroutine that incorporates the complex Bauschinger effect. The results indicate that an accurate material constitutive representation is crucial for better and more accurate prediction and understanding of residual stresses induced by autofrettage processes. Computer modeling based on the true material constitutive representation will likely prove to be a powerful tool for the design of autofrettage processes in general and thick-walled cylinders in particular.

Calculating the grain size effect during strain hardening through a probabilistic analysis of the mean slip distance in polycrystals

Grain refinement is an important mechanism to produce stronger alloys. Strain hardening is an essential phenomenon in metal forming processes. The interaction between grain size and strain hardening is evident: a decrease in grain size (dg)causes an increase in ultimate tensile strength but a decrease in uniform elongation. The Kocks-Mecking (KM) model for strain hardening is based on the relationship between shear strain and the path length for dislocation slip. It provides good general estimates for stress-strain curves, and empirical modifications have been made to include dg. Here, the empirical approach is substituted by theoretical probability calculations, accounting for the fact that the grain size imposes a bound on the mean slip distance, while strain compatibility defines a relationship between grain boundary-dislocation interaction and bulk storage and annihilation. The resulting differential only uses the two parameters inherent to KM. Fitting to published tensile curves for Al, Cu, and Ni produces excellent results. The fitting parameters allow to predict the tensile strength as a function of dgto good approximation, for dg>1μm. Below this limit, fundamental changes in dislocation statistics impose the activation of grain boundary dislocation sources and may induce dislocation density gradients, which seem to determine the flow stress in the sub-μm range.

Mastering the art: Proficient finite element implementation and robust evaluation of a strain-hardening porous ductile material crack growth prediction model at finite strain

Accurate prediction of crack extension is crucial for ensuring the structural integrity of metal components exposed to diverse loads. While the Gurson model and its extensions are widely accepted for delineating ductile fracture stages, especially in porous materials with a rigid-perfectly plastic matrix, their efficacy diminishes in the presence of strain-hardening matrices. To address this limitation, our study introduces a robust numerical implementation and assessment of Perrin's model. In contrast to Gurson's approach, Perrin's model incorporates two distinct strain-hardening parameters derived from an intricate analysis of a strain-hardening hollow sphere subjected to axisymmetric loading.Moving beyond theoretical discussions, this paper actively engages in the rigorous evaluation of Perrin's model under various scenarios, encompassing isotropic, kinematic, and mixed isotropic-kinematic hardening conditions. The model's effectiveness is convincingly demonstrated through meticulous comparisons between numerical simulations and real-world experimental observations conducted on pre-cracked specimens.Facing challenges related to achieving global elastic-plastic convergence in large-scale simulations, our research introduces a sophisticated approach. Leveraging stiffness tangent moduli ensure the maintenance of quadratic convergence in global Newton method iterations. This not only enhances the reliability of our simulations but also underscores the practical applicability of our findings.The study also focuses on the necking and crack propagation of a cylindrical specimen through meticulous computational modeling. Our mesh captures intricate details and addresses stress gradients, revealing coplanar crack propagation contrary to prior beliefs. The confirmation of the cup-cone fracture effect challenges previous interpretations, emphasizing the critical role of void nucleation. This reinforces the credibility and applicability of our approach in advancing the understanding of material fracture behavior.In summary, this study significantly contributes to existing knowledge in fracture prediction models, offering a robust framework for predicting ductile fracture under substantial deformations. The presented findings pave the way for advancements in structural engineering, providing invaluable insights for optimizing the performance and resilience of metal structures in real-world applications.

A machine learning constitutive model for plasticity and strain hardening of polycrystalline metals based on data from micromechanical simulations

Machine learning (ML) methods have emerged as promising tools for generating constitutive models directly from mechanical data. Constitutive models are fundamental in describing and predicting the mechanical behavior of materials under arbitrary loading conditions. In recent approaches, the yield function, central to constitutive models, has been formulated in a data-oriented manner using ML. Many ML approaches have primarily focused on initial yielding, and the effect of strain hardening has not been widely considered. However, taking strain hardening into account is crucial for accurately describing the deformation behavior of polycrystalline metals. To address this problem, the present study introduces an ML-based yield function formulated as a support vector classification model, which encompasses strain hardening. This function was trained using a 12-dimensional feature vector that includes stress and plastic strain components resulting from crystal plasticity finite element method (CPFEM) simulations on a 3-dimensional RVE with 343 grains with a random crystallographic texture. These simulations were carried out to mimic multi-axial mechanical testing of the polycrystal under proportional loading in 300 different directions, which were selected to ensure proper coverage of the full stress space. The training data were directly taken from the stress–strain results obtained for the 300 multi-axial load cases. It is shown that the ML yield function trained on these data describes not only the initial yield behavior but also the flow stresses in the plastic regime with a very high accuracy and robustness. The workflow introduced in this work to generate synthetic mechanical data based on realistic CPFEM simulations and to train an ML yield function, including strain hardening, will open new possibilities in microstructure-sensitive materials modeling and thus pave the way for obtaining digital material twins.

Creep Behavior of the Clay Cores at the Bougdoura Dam Using Ansys Software

Abstract The creep of fine soils is due to the viscous properties of the assembly of mineral particles accompanied of adsorbed water which forms intergranular skeleton. It is evident during the secondary consolidation that the effective stresses are constant, the deformation extends over time. Rock fill dams with clay sealing cores deformed during exploitation. During commissioning of the core, clay undergoes. Creep is a major characteristic of the nonlinear behaviour of materials, in which the material continues to become deformed under a constant load. It can cause considerable deformations of the works (two to three times instantaneous strain in three years). This study presents a prediction of the creep behavior of a clay core in a rock dam subjected to constant hydrostatic loading for 20000 h and describes a procedure for modeling the primary and secondary creep law simulation using ANSYS software APDL In this aims, we have applied the finite element method based on a model shown in equation 8 called (Strain Hardening Model) in order to simulate a creep behavior of clay core.

Insights into building a digital twin of closed-cell aluminum foam during impact loading: Microstructural, experimental and finite element investigations

The mechanical behavior of metal foams under impact loading depends on multiple and complex parameters like impact velocity, strain-rate, local plastic deformation, oscillating and micro-inertial effects, etc. The prediction of the behavior of metal foams that are subject to impact loads is still challenging and engineering application of these materials typically requires time-consuming experimental tests. Numerical models based on the finite element method (FEM) can contribute to minimizing the experimentation effort. Realistic FEM models were built that account both for the macro- and micro-scopic characteristics of the porous material, explain the acting mechanisms that take place during impact, and study the yield properties as well as the energy absorption during the impact of closed-cell aluminum foams. The simulation results are compared with the ones derived from respective experimental uniaxial tests. Two different modeling approaches were applied thus creating two models. The first model relies on a cell-based method where the initial geometry of the foam was generated based on the Voronoi tessellation algorithm and the second one relies on the isotropic, strain-hardening, and continuum-based model developed by Deshpande-Fleck. The outcome of the investigation sheds light on the metal foam behavior under impact by explaining macro- and micro-structural phenomena that develop during impact.

Towards the work hardening and strain delocalization achieved via in-situ intragranular reinforcement in Al-CuO composite

Dense intragranular distribution of nanoscale reinforcements is highly desirable since it is effective in reconciling the strength-ductility trade-off in Al matrix composites (AMCs). Herein, we report a systematic investigation on the work hardening and strain delocalization in Al-5 wt.% CuO (Al-5CuO) composite with strength-ductility synergy contributed by in-situ dense intragranular nanoscale Al2O3. Results reveal that Al-5CuO exhibits prominent hetero-deformation induced (HDI) strengthening as indicated by its larger HDI stress than effective stress. We showcase that the notable pile-ups of geometrically necessary dislocations (GNDs) at intragranular Al2O3 result in the prevailing kinematic hardening. While the plastic relaxation dislocations (PRDs) around Al2O3 generated by the release of GND-induced internal stress produce isotropic hardening. Both contribute to the pronounced work hardening of Al-5CuO. Comprehensive characterizations suggest the GND distribution with marked intragranular feature in Al-5CuO during straining, which implies the effective provoking of grain interior rather than grain boundary (GB)/interfacial zone to take plastic strain. On basis of the well-described storage and annihilation of GNDs and PRDs at the intragranular Al2O3, the microstructure-based strain-hardening model enables an in-depth understanding of the kinematic and isotropic hardening contributions by Al2O3 in Al-5CuO. Systematic analysis further confirms the important roles of intragranular Al2O3 in improving the strain partitioning, strain/stress transfer and strength matching across different domains of Al-5CuO, which significantly contributes to strain delocalization and hence strength-ductility synergy. This work sheds important insights on the innovative design of strong and ductile AMCs with intragranular nanoscale reinforcements for structural applications.

Effect of rock nonlinear mechanical behavior on plastic zone around deeply buried tunnel: a numerical investigation

Rock shows a significant nonlinear mechanical behavior in the deeply buried tunnel, and it could affect the stress redistribution and the magnitude of the plastic zone (PZ) around the tunnel. Therefore, a series of numerical simulations were performed to highlight the effect of rock nonlinear behavior on PZ with the implementation of a novel proposed unified strain-hardening and strain-softening (UHS) constitutive model. UHS model can well describe the nonlinearity of stress–strain curves, peak strength and residual strength. The numerical model was first validated via the experimental results of one model test, followed by the parameter sensitivity of UHS model and initial stress field. The effect of strain-hardening, strain-softening, the nonlinearity of peak and residual strengths of rock, buried depth of tunnel and the lateral pressure coefficient were discussed. A detailed description method of the PZ was finally proposed considering the nonlinearity of rock. The results reveal that (i) PZ can be divided into the residual zone, strain-softening zone and strain-hardening zone; (ii) the maximum tangential stress stays in the strain-hardening zone; (iii) the initial stress state can change the shape of PZ. Moreover, for the deeply buried tunnel, the pre-stressing measures show a good potential to control PZ, and the support should be applied as early as possible to reduce the relief of initial stress.

Machine learning quantum-chemical bond scission in thermosets under extreme deformation

Despite growing interest in polymers under extreme conditions, most atomistic molecular dynamics simulations cannot describe the bond scission events underlying failure modes in polymer networks undergoing large strains. In this work, we propose a physics-based machine learning approach that can detect and perform bond breaking with near quantum-chemical accuracy on-the-fly in atomistic simulations. Particularly, we demonstrate that by coarse-graining highly correlated neighboring bonds, the prediction accuracy can be dramatically improved. By comparing with existing quantum mechanics/molecular mechanics methods, our approach is approximately two orders of magnitude more efficient and exhibits improved sensitivity toward rare bond breaking events at low strain. The proposed bond breaking molecular dynamics scheme enables fast and accurate modeling of strain hardening and material failure in polymer networks and can accelerate the design of polymeric materials under extreme conditions.

A novel semi-analytical solution to ground reactions of deeply buried tunnels considering the nonlinear behavior of rocks

The nonlinearity of rock becomes more significant as the buried depth increases, which changes the stress redistribution and deformation patterns during tunneling. In this study, a newly proposed UHS model (unified strain-hardening and strain-softening constitutive model) and the finite difference method are applied to obtain a novel semi-analytic solution that is used to investigate the effects of nonlinear characteristics such as strain-hardening and strain-softening on the ground reaction. The yield surface and the plastic internal variable of the calculated node are consistent and are solved by iteration. The solution of differential equations is unnecessary. Therefore, the proposed solution can be used to accurately calculate the plastic internal variable and the stress state in the plastic zone without stress vibration in the strain-hardening zone that was often observed in previous solutions. The proposed model is validated via comparison to the classical solution and numerical results. Then, the influences of strain-hardening, strain-softening, and prestress on ground reactions are highlighted. The radius of the plastic zone and the displacement of the tunnel wall gradually decrease with increasing post-peak ductility. Considering strain-hardening characteristics would increase the radius of the plastic zone. Moreover, prestressing significantly reduces the plastic zone radius and tunnel wall displacement in deeply buried tunnels.

Numerical implementation and application of an internal state variable model to analyze the time-dependent behavior of mining excavations in rock salt

The geomechanical behavior of rock salt has been investigated extensively over the years. Experimental studies have identified distinctive features associated with nonlinear inelastic response that shows strong time and loading history dependencies. In this paper, a relatively simple constitutive model is presented and implemented into the numerical code FLAC, and then applied to analyze the time-dependent behavior of excavations in salt mines. The unified creep-plasticity model includes an internal state variable (ISV) with an evolution law that induces progressive strain hardening (SH) until a steady state is reached. Numerical analyses are performed with the proposed ISV–SH model to evaluate material parameters, based on creep test results on natural rock salt, and to simulate the response of a circular opening and of rectangular mining excavations created in sequence. The results are analysed and compared with those obtained with the well-known Norton power law equation, commonly used in salt mine engineering. The time-dependent calculation results illustrate key aspects of rock salt behavior and highlight the major influence of transient inelastic behavior and stress redistribution on the response of underground openings. The proposed modelling approach constitutes an advantageous alternative to analyses based on stationary creep laws, often used in rock salt mining operations.

Mechanical Properties and Strain-Hardening Models of Supermartensitic Stainless Steels Alloyed to Nitrogen and Vanadium

Mechanical Properties and Strain-Hardening Models of Supermartensitic Stainless Steels Alloyed to Nitrogen and Vanadium

Flexural response of TRM subjected to low-velocity impact loads: Experimental and analytical study

A constitutive approach to investigate the flexural impact performance of textile-reinforced mortar (TRM) is presented in this study. Experiments were performed under three-point bending conditions on a drop-weight impact system at 1, 2, 3, 4, and 4.5 m/s. Experimental results showed that the differences in peak load from 4.5 to 1 m/s were 1.964 kN (for BTRM-4) and 2.191 kN (for BTRM-6), and in energy absorption from 4.5 m/s to 1 m/s incident velocities were 2.66 J (for BTRM-4) and 2.98 J (for BTRM-6). Additionally, analytical modeling of experimental results was performed to identify the correlation between the experimental and analytical results. The parameters for a strain-hardening material model were obtained by using closed-form equations. The prepared model could reproduce a tripartite load-displacement response related to pre-cracking and post-cracking behavior. The results also verified that the best agreement between the analytical model and experimental data was achieved by considering scattering, softening, and reinforcement waviness in cement matrix under different loadings. The tensile properties of the tested samples were predicted by using an inverse algorithm and model parameters. Notably, the parametric model overpredicted the simulated three stages of TRM composites. Results could be used as average load values in the structural design and analysis of cement-based material composites under different impact loads.

Loading-Unloading Behavior of a Spherical Contact for Varying Tangent Modulus and Yield Strength

Abstract Understanding the elastoplastic contact loading-unloading behavior between a sphere and a rigid plane is a problem in the field of contact mechanics. In this study, a bilinear strain-hardening material model was used to study the frictionless elastoplastic contact loading-unloading behavior of a sphere in contact with a rigid plane across a large range of interference. A two-dimensional axisymmetric finite element model was established. The effects of the tangent modulus (Et) and the ratio of the reduced elastic modulus to the yield strength (E/Y) on the contact load, residual interference, and contact area of the spherical contact model during loading-unloading were analyzed for a series of different interferences. The effects of Et and E/Y on the elastoplastic contact loading-unloading behavior were amplified with increasing interference. With an increase in Et, the effect of E/Y on the contact behavior was diminished. A new constitutive model for elastoplastic contact loading-unloading is presented. The model accommodates the calculation of the contact load, contact area, and residual interference of the spherical contact model across a large range of interference. The proposed model was verified by comparing its predictions with those of previous models. In the range of material properties considered in this work, the current research results can be applied to particle and contact mechanics.

A predictive model for strain hardening and inertia effect of aluminum tubes filled with aluminum foam

Studies on strain hardening and inertia effect of foam-filled tube (FFT) remain limited. Therefore, this work has conducted mesoscopic finite element analyses on FFTs. The 7075-T651 aluminum alloy is chosen for tube material and the 1100-H14 aluminum is employed for the base material of closed-cell foam. The deformation mechanism of the interaction between tube and foam, and the inertia effect on compressive response of FFTs, are both revealed. Results show that due to the interaction, FFT has a higher compressive stress compared with the sum of empty tube and individual foam under the same mass. As more material is involved, the load-bearing capacity, strain hardening, and interaction stress of FFTs all increase with the relative density of infilled foam. A predictive model is established to predict the compressive stress and strain hardening of FFTs. The load-bearing capacity of tube, the plastic hardening of foam, and the interaction effect between tube and foam are all considered in this model. Moreover, due to the inertia effect, the stress at the impact end is significantly higher than that at the support end under high-velocity impact. The one-dimensional shock wave theory is added to the model, enabling the prediction under high-velocity impact.

Characterization of double strain-hardening behavior using a new flow of extremum curvature strain of Voce strain-hardening model

Characterization of double strain-hardening behavior using a new flow of extremum curvature strain of Voce strain-hardening model