Equivalent Plastic Strain Research Articles

A new unified creep‐plasticity constitutive model coupled with damage for viscoplastic materials subjected to fatigue loading

AbstractA new unified creep‐plasticity (UCP) constitutive model coupled with damage is proposed for Sn–3.0Ag–0.5Cu (SAC305), one of the most successfully commercialized Pb‐free solders. By calibrating the proposed damage model based on entropy generation, the fatigue issues are elucidated for SAC305 solder at different temperatures and strain rates. After implementing a user‐defined material subroutine, finite element simulations with the proposed UCP‐damage model are capable of predicting the strength deterioration as the macroscopic response in terms of load‐deformation curves. More importantly, the UCP‐damage model reveals the damage accumulation and evolution of viscoplastic materials sensitive to fatigue deformation at different temperatures and strain rates. By comparing the predictions with and without damage, the equivalent plastic strains are obviously different when evaluating the thermal cycling fatigue life of electronic packaging structures, which confirms the significance of the UCP model reasonably coupled with the intrinsic description of damage by the concept of entropy generation.

Effect of Pre-Strain on Crack Growth Behavior of Zr702/TA2/Q345R Composite Plate

The influence of pre-strain on the fatigue crack growth behavior of Zr702/TA2/Q345R composite plate is studied by experiments and the finite element method. The crack perpendicular to the interface and the through-wall crack are considered at the same time. For the crack perpendicular to the interface, the monotonic plastic zone and cyclic plastic zone at the crack tip are used to study the influence of pre-strain on the plastic zone. Furthermore, the influence of pre-strain on the evolution of the plastic damage at the crack tip is analyzed in detail by studying the variation in the initial plastic energy and equivalent plastic strain. For the through-wall crack, the effect of pre-strain on the propagation behavior of cracks on both sides and the whole crack is studied systematically. The results show that the strengthening of the cracks on the Zr702 side is significantly higher than that on the Q345R side, so the inhibitory effect of pre-strain on the whole crack of the through-wall specimen is mainly due to the increase in the resistance to crack growth on the Zr702 side.

Failure analysis of polytetrafluoroethylene lined pipe under thermal shock

In the process of fluid transportation, polytetrafluoroethylene (PTFE) lined pipe is subject to constant thermal stress caused by constant temperature fluid and alternating thermal stress caused by alternate flow of cold and hot fluid, making it susceptible to progressive plastic strain accumulation, namely the ratcheting. In this paper, cold and hot shock tests of PTFE lined pipe at different temperatures were carried out. Ohno-Wang II model was used to predict the ratcheting of PTFE lined pipe under cyclic temperature loading. The simulation result shows that the ratcheting strains occur in the same position as the test result. The equivalent plastic strain control method was used to determine the ratcheting boundary temperature as 145 °C and 90 °C for PTFE lined pipes under cold and hot shock respectively. The ratcheting boundaries of lined pipe with different PTFE lining thickness were given to obtain the influence of lining thickness on ratcheting boundary.

Understanding the bending behavior and through-thickness strain distribution during asymmetrical rolling of high-strength aluminium alloy plates

The asymmetric rolling (ASR) process is highly desired to improve the through-thickness deformation/strain uniformity by introducing additional shear strains for uniform through-thickness microstructures and mechanical properties of metallic/alloy plates. In this study, the bending behavior and mechanism during the ASR processing of high-strength AA7050 aluminium alloy plates were simulated along with rolling trials. It shows that the plate will bend upward (toward slower roll) at larger speed ratios and smaller thickness reductions but downward (toward faster roll) at smaller speed ratios and larger thickness reductions. The ASR processing can increase the central equivalent plastic strains and decrease the surface-to-center strain gradient compared with that caused by the conventional symmetric rolling. The high strain rate bands (HSRBs) as key plastic strain accumulation regions are intimately connected with the post-rolling equivalent plastic strain distribution and the outgoing curvature. Especially, when the HSRB approaches the plate upper surface near the end of the deformation zone, normally at larger thickness reductions, a downward bending occurs despite that the lower roll rotates faster, and vice versa. The through-thickness HSRB induced by the ASR processing is considered to mainly enhancing the equivalent plastic strain homogeneity. The formation and interactive mechanisms of the HSRBs and their connection with the bending behavior during the ASR processing were discussed.

Approximate residual stress and plastic strain profiles for laser-peened alloy 600 surfaces

This paper presents approximate in-depth residual stress and plastic strain profiles for laser-peened alloy 600 surface via FE analysis. In approximations, effects of the initial welding residual stress and the number of shots are quantified. Based on FE analysis results, residual stress profiles are quantified by two variables; the maximum difference in stress before and after LSP, and the depth up to which the compressive residual stress exists. Plastic strain profiles are quantified by one variable, the maximum equivalent plastic strain at the surface. The proposed profiles are validated by comparing with published LSP experimental results for welded plates. Effects of the initial welding residual stress and the number of shots on these variables are discussed. The proposed profile can be directly applied to predict the mitigation effect of LSP on PWSCC and to efficiently perform structural integrity assessment of laser peened nuclear components.

Towards material flow prediction in friction stir welding accounting for mechanisms governing chip formation in orthogonal cutting

A new approach to integrate the damage in a 3D friction stir welding model within the coupled Eulerian–Lagrangian (CEL) framework is proposed. The novelty is represented by the employed damage criteria accounting for the mechanisms governing chip formation in orthogonal cutting. Material flow is correctly predicted with the new approach avoiding the problems encountered when neglecting damage or when including it through the traditional approach (Johnson–Cook failure criterion for initiation and energy criterion for evolution). The model can simulate in-plane forces and nugget zone width according to the experiments. The maximum equivalent plastic strain is estimated in the flow arm zone, due to the simultaneous action of pin and shoulder. Additionally, it is demonstrated the importance in mesh element size if material flow is investigated through CEL models. The elements in the interaction zone must be sufficiently small for describing the cyclical layer deposition at each tool rotation.

Effects of support type and geometric shape of steel tube on concrete-encased concrete-filled steel tube beam under low velocity impact

Concrete-encased concrete-filled steel tube (CEFST) beams prepared by placing steel tube in RC beam is a beam type that has widespread use. The current study examines the effects of steel tube geometry and support conditions on the behavior of CEFST beams under low velocity impact loading. First, CEFST beam specimens with different lengths and different tube section geometries (circular and square) were produced in the laboratory. These four test specimens with two different support conditions were exposed to low velocity impact load tests. Finite element models of the test specimens were created using Abaqus\\Explicit software. In the next stage, 4 finite element models were verified by the experimentally obtained damage conditions, maximum displacements, and support reaction forces. In the final stage, as parametric study 12 finite element models were prepared in addition to 4 verified models and analyzed under low velocity impact loading. In addition to experimental values, Von Mises stresses, Equivalent plastic strain, Friction energy, and Damage energy values were also obtained by the numerical study and thus the effects of steel tube geometry and support conditions were comparatively examined. The obtained results showed that CEFST beams with a square tube section exhibited better performance under a sudden load such as impact compared to the beams with a circular tube section. Moreover, both numerical and experimental results pointed out that the beam length beyond support has a positive impact on the performance of beam under impact loading.

The influence of material model on the neck development for aluminium alloy sheet

The neck development for bore expansion problem is analyzed. Static implicit calculations are carried out for the A2219 Aluminium alloy sheet using ABAQUS/Standard. The equations to give the conditions of the onset of the localized necking of sheet metal based on the general bifurcation theory are presented for plane stress. Since accurate calculation of stresses and strains are the basis for the necking prediction, both associated and non-associated flow rule are adopted in the material model in which Hill’s quadratic functions are used. User defined subroutine UMAT is developed using a fully implicit integration scheme. The results of necking prediction show that necking occurrence delays for the Hill solid using both AFR and NAFR based model compared with Mises solid and necking occurrence slightly delays for the Hill solid using AFR based model compared with Hill solid using NAFR based model. Initial necking occurs when equivalent plastic strain is respectively 0.33, 0.39 and 0.348 for the Mises solid and Hill solids using AFR and NAFR based models. Theses indicate that the material model has significant influence on the accuracy of necking prediction.

Evaluation of elastic-plastic deformation in HSS work roll under coupling of residual stress thermal stress and contact stress during hot rolling

Fatigue damage such as crack and spalling on the work roll surface in hot rolling is caused by comprehensive action of residual stress, thermal stress and contact stress. In this work, a HSS work roll was studied based on the actual hot rolling condition, and high temperature performances of the work roll materials are considered. Finite element method was used to obtain the residual stress distribution of the work roll after quenching and tempering. Then, the coupling mechanism of residual stress, thermal stress and contact stress of the work roll in the bite region are analyzed by a transient thermomechanical model. The results showed that, the maximum equivalent strain and equivalent plastic strain appear at the exit of the bite region. And residual stress and thermal stress account for about 90% of the coupling stress. The accumulation of plastic deformation only occurs in the initial rolling, and the initial temperature influences the plastic deformation accumulation. Furthermore, abnormal rolling often leads to large plastic deformation on the roll surface.

Forecasting the Fatigue Strength of DC01 Cold-Formed Angles Using the Anisotropic Barlat Model

The objective of this work is to present the numerical simulation of the air-bending process of DC01 steel. There are plenty of works concerned with assessing the springback phenomenon in the bending process also using anisotropic material models (Hill's model is widely used). However, very few recent publications are concerned about the fatigue life assessment of bent products. As ensuring the proper fatigue resistance of products is vital for increasing safety and widening the service intervals there is certainly a need to perform investigations in this field. In this work, the air bending simulation of anisotropic DC01 steel with the usage of Barlat's plastic anisotropy model was presented. Together with springback analysis and the equivalent plastic strain cumulation during incremental bending. Strain cumulation is believed to be an important factor in predicting fatigue life. It was shown that the strain development rate depends on the bending process parameters, especially from the bending line orientation to the sheet rolling direction.

Residual stress analysis and its effect on springback for multi-step pressbrake bending

Pressbrake bending is a multi-step metal forming process and widely applied in the fields of aerospace, shipbuilding, and offshore industry. However, the bending residual stress that arise from the previous-pass bending step will affect the stress distribution of the next-pass bending step, and finally affect the springback after unloading, which results in the difficulty to guarantee the dimensional accuracy of the forming part. In this study, the residual stresses for multi-pass pressbrake forming and its influence on springback are systematically investigated. First, the analytical model for the residual stress of the bent specimen with initial curvature is deduced based on geometric relationship and elastic–plastic bending theory. Second, the calculation method of rigid body position redefine to simulate the multi-pass bending forming process is developed, and the numerical method is confirmed by comparison with experimental method. The analytical model to predict the residual stress is shown to be in close agreement with results from numerical method, demonstrating the validity of the analytical model. Finally, the impact of residual stress in single-pass and multi-pass bending forming on springback are discussed thoroughly. It is found that, as the number of forming passes increases, the equivalent plastic strain will increase to 9% of three-pass loading from 7.8% of one-pass loading, which explains the reason of increasing the number of bending passes can not only reduce springback, but also reduce the residual effect of bending forming.

Study on fracture behavior of pipeline girth weld based on CTOD-Am method and Gurson ductile damage model

The mechanical properties of the materials in different regions of the pipeline girth weld are sometimes quite different, which will produce a more significant material constraint effect and complicate the fracture behavior of the girth weld. Therefore, this work adopts the finite element method combined with the material damage model to study the ductile tearing process of the weld. The results of the single edge notched bending (SENB) specimens with the weld center crack show that for the welds with different mismatch conditions, with the increase of the weld mismatch coefficient, the crack tip constraint decreases gradually, and the fracture toughness increases gradually. The smaller weld width will make this effect more significant. When the ratio of the weld width to the specimen width is larger than or equal to 0.43, the BM will basically no longer affect the crack tip constraint and the fracture toughness of the weld. The results of the SENB specimens with the interface crack show that for the overmatched weld, with the increase of the weld mismatch coefficient, the crack first grows along the interface and then deflects into the heat affected zone (base metal). When the weld mismatch coefficients are 1.44 and 1.86, the corresponding deflection angles are 14.84° and 24.61°. For undermatched weld, with the decrease of the weld mismatch coefficient, the crack growth will deflect into the weld metal. When the weld mismatch coefficients are 0.69 and 0.6, the corresponding crack growth deflection angles are 14.04° and 25.36°. The larger the degree of the weld mismatch, the more significant the deflection of the distribution of the equivalent plastic strain and the stress triaxiality ahead of the crack tip. The effect of the specimen thickness on the deflection angle of the interface crack growth is small. The verification shows that the numerical analysis results of this study are valid.

A ductile fracture model incorporating stress state effect

To understand comprehensively the relationship between material ductility and stress state, the new shear, shear-compression, and shear-tension specimens were specially designed, and seven types of specimens were used in total to achieve precise control of stress states over wide ranges of stress triaxialities and Lode angle parameters. A hybrid experimental-numerical method was employed to determine the equivalent plastic strain, stress triaxiality, and Lode angle parameter, and hence to construct the 3D fracture locus of the Ti-6Al-4V alloy. Different micromechanisms were found to dominate the failure process under various stress states. Based on the experimental results, a new ductile fracture model coupling both stress triaxiality and Lode angle parameter was proposed and implemented into the commercial finite element program ABAQUS/Explicit via the user material subroutine VUMAT. Comparative studies with some other fracture criteria indicate that the proposed fracture model can capture the non-monotonic feature of fracture strain, and predict the fracture strain with better accuracy in a wide range of stress states. A verification test was performed to check the predictive capability of the present model. The results show the excellent agreement between experiment and simulation with respect to the fracture displacement and fracture morphology. This study paves the way for characterizing and predicting the ductile behavior of metallic materials under complex stress states, and provides a fundamental databank for the analysis and design of Ti-6Al-4V alloy structures.

Toward robust scalar-based gradient plasticity modeling and simulation at finite deformations

Strain gradient plasticity has been the subject of extensive research in the past 40 years in order to model size effects in metal plasticity, on the one hand, and provide finite width shear bands in the simulation of localization phenomena, on the other hand. However, the use of the emerging models is still limited to academic applications and has not yet been adopted by industry practitioners. The present paper systematically reviews the pros and the cons of gradient plasticity at finite strains based on the gradient of scalar plastic variables, in particular the gradient of the cumulative plastic strain. It proposes benchmark tests addressing both size effect modeling and plastic strain localization simulation. It includes new analytical solutions for validation of FE implementation. It focuses on the micromorphic approach to gradient plasticity, as a convenient method for implementation in FE codes. New features of the analysis include the comparison of three distinct formulations of rate-independent gradient plasticity at finite deformations, based on the multiplicative decomposition of the deformation gradient and on quadratic potentials with respect to gradient terms. The performance of micromorphic and Lagrange-multiplier-based strain gradient plasticity models is evaluated for various monotonic and cyclic loading conditions including confined plasticity in simple glide and tension, bending and torsion at large deformations. Limitations are pointed out in the case of bending and torsion, which can be overcome for instance by the use of the gradient of equivalent plastic strain model.

Parametric investigation of micro-pores coalescence in the microstructure of LPBF manufactured AISI 316 stainless steel under high cycle fatigue loading

In this study, damage growth and load-carrying capacity of specimens made by laser powder bed fusion (LPBF) at various triaxial stresses have been evaluated by the damage mechanics approach, using the Chaboche-Lemaitre stress-based damage model and Lemaitre damage model based on equivalent plastic strain under high cycle fatigue (HCF) loading. In this regard, with the development of a parametric numerical model, the effect of stress triaxiality, external HCF loading, and micro-pore geometric parameters size on the damage growth and coalescence of two-void cluster embedded in representative volume element (RVE) have been investigated. The results show that increasing the triaxial stress from 0.5 to 2.1 leads to a severe decrease in ligament load carrying capacity and eventually voids coalescence through an increase in von Mises stress around the micro-pores. The results also indicate that a two-void cluster with a relative distance of less than 10 can be considered as a crack initiating site in the microstructure of LPBF components under HCF loading.

Numerical Simulation of Rock Breaking by Single Worn Cutting Tooth

The cutting teeth on PDC bits have been working under wear for a long time, but the understanding of their rock breaking mechanism is not deep enough. In this paper, the influence of key factors such as wear height, passivation type, invasion depth, lithology, rake angle and tooth diameter on the load distribution of the cutting tooth edge, as well as the equivalent plastic strain form of the rock section, are investigated by means of numerical simulation. The results show that under the same rock breaking parameters, with the increase of wear height, the stress concentration at both ends of the cutting tooth edge is obvious, and the load in the middle section of the cutting tooth edge decreases with the increase of wear height, and the load fluctuation of the cutting tooth edge increases; The load on the tooth edge of the worn cutting gear decreases with the increase of the tooth diameter, and the fluctuation of the load on the tooth edge increases; The load distribution of the cutting tooth edge with an inclination of 15° is uniform, while the stress concentration at both ends of the cutting tooth edge with an inclination of 10° and the load drop at the middle section are obvious; Compared with the cutting teeth of the other two types of wear, the conventional wear cutting teeth have longer effective rock breaking length, larger load on the cutting edge, more uniform distribution and better rock breaking effect; According to the relevant simulation results, it is believed that the wear height, design parameters and wear types will affect the size and distribution of the tooth edge stress in the cutting process of worn cutting teeth, and then affect the wear trend in the cutting process. In addition, by observing the equivalent plastic strain form of the rock section after cutting, it is found that the rock cuttings under the action of new teeth are semicircular blocky, while the rock cuttings under the condition of worn teeth are flake. It is believed that the new teeth are more likely to form large blocky rock cuttings in the process of rock breaking, and the rock breaking effect is better than that of worn teeth.

Generation of fine extension twins in rolled magnesium alloy AZ31B at room temperature by simple shear

A textured AZ31B plate was subject to simple shear along 45° to its normal direction at room temperature, and extension twinning under biaxial stress was investigated by statistical analyses of electron backscatter diffraction maps. Extension twinning is the primary deformation mechanism up to a plastic shear strain of 15% (8.66% equivalent plastic strain), and the most frequent twin thickness remains to be 1.5 μm. The simple shear suppresses twin growth, yet brings sustained twin nucleation. The critical resolved shear stress of extension twinning is determined as 25 MPa and remains virtually constant up to a plastic shear strain of 10%. The present study suggests that by using biaxial stress state that promotes multi-twin nucleation, a microstructure with dense and fine twins can be produced at room temperature in a conventional Mg alloy, without jeopardizing the contribution of twinning to plastic straining.

Research on warm laser shock sheet micro-forging

This paper introduces warm laser shock sheet micro-forging, which combines the advantages of sheet bulk metal net forming, laser shock dynamic micro forming and warm forming. The influence of AZ31B magnesium alloy on laser energy and forming temperature was investigated by experiment and simulation. The mechanism that warm temperature has better properties than room temperature has been revealed from the aspects of microstructure, stress wave transmission and material flow. The results show that the forming depth of workpiece increases with the increase of laser energy. Forming depth increases with increasing temperature at the same laser energy, but serious ablation occurs on the surface of workpiece at 250 °C, which affects the forming quality of workpiece. EBSD results show that with the increase of forming temperature, the number of twins decreases, the dislocation density decreases and the forming depth increases. The grain refinement after laser shock forming is obvious, and the increase of grain dislocation density promotes the improvement of microhardness, which indicates that laser shock can improve the mechanical properties of materials. The numerical simulation results show that the elastic wave propagates faster than the plastic wave. The stress on the workpiece at 150 °C is less than that at room temperature, but the equivalent plastic strain is higher than that at room temperature. After plastic deformation, the material in the workpiece gradually flows to the cavity. At 150 °C, the material flow inside the workpiece is faster, the filling effect is better and the forming uniformity is better.

Axial mechanical behavior of an innovative liftable connection for modular steel construction

Modular steel construction (MSC) exhibits widespread potential applications in civil engineering due to its quickness and standardization. Inter-module connection is a crucial issue for the structural behavior of MSC. A new fully prefabricated liftable connection (FPLC) for MSC was proposed in this paper. Axial compressive loading tests of the FPLC were conducted. Followed, an elaborate finite element model (FEM) for the FPLC was developed. Validation of the FEM by three test specimens confirmed that the developed FEM was capable of predicting the load bearing capacity and failure mode of the FPLC. Furthermore, the validated FEM was used to conduct a series of simulations on the tensile performance of the FPLC to perform an in-depth investigation on the influence of the thickness of the gusset plate (tp), thickness of the inner plate (ts), strength grade of the column (Sc), pretension load of the long stay bolt (P), diameter of the long stay bolt (d) and thickness of the modular column (tc). The influence of these parameters on the ultimate axial tensile resistance of the FPLC and damage indices, including the rupture index (RI) and plastic equivalent strain (PEEQ), along the defined critical lines of all specimens was determined and is reported and discussed in detail to reveal the damage mechanism of the connection under tensile force. Finally, a theoretical model for predicting the ultimate axial tensile resistance of the FPLC was proposed. The capability of the formulas to predict the axial ultimate tensile resistance of the FPLC was checked through validation against a total of 16 numerical results. The present study provides an engineering practical connection for MSC and important guidance for the design of the connection.

Variable Factors Affecting Progressive Destruction of Composite Steel Tall Building

In recent years, the presence of progressive collapse in tall buildings induced a catastrophic event which attracted the majority of the community’s attention. The purpose of this paper is to develop a 3D numerical analysis of tall building under column loss. A composite steel frame building with 25 stories with five spans in both directions is proposed. The building has 3 m story height and 8 m span in both directions. The building is designed through the commercial software SAP2000 software against wind loads based on Eurocode 1-2005. The focus here is to investigate various parametric studies under abrupt column loss of multi-story composite building. The effect of composite slab is considered with full composite action between beam and slab. The findings of a parametric formulation incorporating important parameters for the progressive collapse design technique are given and confirmed using nonlinear dynamic time history analyses. The assessment of results has been introduced based on deformation, axial force in columns, equivalent plastic strain, major moment and axial force in the considered beams above the column loss. Next, a probabilistic analysis has been performed to assess the behavior of composite steel buildings against column loss. The study investigates the critical column loss and pinpoints the location of the next critical column. The results show that the concrete grade, position of the removed column, beams cross-section, and place of bracings have a significant effect in the response of the building rather than the steel grade and bottom reinforcement density. The removal of exterior column has the significant increase of the axial force percentage by 111.4% for the corner column. The corner column removal gives the maximum equivalent plastic strain with a value of 0.00449. Furthermore, the results reveal the potential impact of uncertainty on the structural elements of the considered buildings through the progressive collapse analysis. The vertical displacement above the column is fitted with mean value of 0.0251387 m and with a coefficient of variation 0.01664.