Effective Plastic Strain Research Articles

Plastic strain effect on cleavage microcracks propagation in probabalistic statement. Part 2. Research results

The second part of the paper presents the results of uniaxial tension testing of smooth round bars of 2Cr–Ni–Mo–V steel in the thermally-embrittled state and St3 steel in the initial state. SEM examination of the fracture surfaces is carried out. The brittle fracture probability is calculated using the Prometey model presented in the first part of this article. It has been found that the plastic strain effect on the microcrack propagation probability is caused by two reasons: (1) the critical brittle fracture stress increase due to formation of new barriers for microcrack under plastic deformation, and (2) the working volume decrease due to the neck formation in tensile round bar. A unified set of parameters has been proposed to take into account the plastic strain effect on cleavage microcracks propagation probability for WWER-1000 RPV steel and low-alloyed low-strength steel.

Plastic strain effect on cleavage microcracks propagation in probabalistic statement. Part 1. Formulation of the problem and research methods

The first part considers the main physical and mechanical processes occurring under tension of round bars. The procedure is presented that allows one to describe the plastic strain effect on the critical brittle fracture stress in probabilistic statement. The main statements of Prometey model for prediction of fracture stress are also presented. The investigations are carried out for two materials: 2Cr–Ni–Mo–V steel used for WWER-1000 RPV in the thermally-embrittled state and low-alloyed low-strength steel of St3 grade taken as model material ruptured by cleavage up to plastic strain up to 50%.

Combining Effective Plastic Strain and Surface Roughness for Predicting Future Propagation Path of Microstructure‐ Sensitive Crack (MSC) in Polycrystalline Nickel

ABSTRACTThis work introduces a damage index (DI) that combines the effective plastic strain and surface roughness changes to predict the future propagation path of a microstructure‐sensitive crack (MSC) in a polycrystalline nickel fatigue sample. The surface topography of a fatigue sample was measured at short fatigue intervals, from which both the effective plastic strain and surface roughness changes were calculated using digital image correlation (DIC). Three DIs based on the effective plastic strain, surface roughness changes, and their combinations were studied using two criteria, that is, the highest intensity and the confidence threshold. Comparing the crack path predicted by these DIs with the actual crack path acquired at later fatigue cycles, we demonstrated that the combined DI is more accurate and has less uncertainty in predicting the future crack path.

Mesoscopic coupled plasticity-damage model of rough surface considering size-dependent plasticity

Metallic materials exhibit significant size effect at mesoscopic scale have been revealed by many experiments. Thus, it is essential to consider size effect when conducting mesoscopic scale studies in tribology. However, there is no constitutive model considering both ductile fracture and size effects of rough surface in the literature. At the same time, the simulation of friction and wear at the mesoscopic scale suffer from computational inefficiency using the conventional theory of mechanism-based strain gradient (CMSG) plasticity theory. To address the aforementioned challenges, we propose a mesoscopic coupled plasticity-damage model by combining the coupled plasticity-damage model and the simplified CMSG plasticity theory. This model can take into account not only the effect of stress state, temperature, strain rate on plasticity and fracture, but also the effect of the effective plastic strain gradient. Meanwhile, the model is able to solve the effective plastic strain gradient by a simplified method, thereby enhancing the computational efficiency. Then, model parameters for bearing bushing material of an engine are calibrated. Finally, scratch simulation and scratch tests of bearing bushing material at the mesoscopic scale are conducted to validate the effectiveness of the mesoscopic constitutive model. The residual scratch depth and width, coefficient of friction at different normal loads are investigated by experiment and simulation, respectively. Results proved the effectiveness of mesoscopic coupled plasticity-damage model, which is applicable for investigating issues related to wear, friction, and contact.

Corrected Method for Scaling the Structural Response Subjected to Blast Load

In scale-down tests of ship structures subjected to a blast load, the accuracy of the predicted response of a prototype is affected by the material substitution and geometric distortion between a scaled model and a full-size structure; this is known as incomplete similarity. To obtain a more accurate response from a prototype during small-size tests, a corrected method for scaling the response of thin plates and stiffened plates under a blast load was derived. In addition, based on numerical simulations of explosion responses by employing the elastic–plastic model and the Johnson–Cook constitutive model, it was found that using the average yield stress derived from the equivalent plastic strain energy in the ideal elastic–plastic model can obtain consistent structural responses. Moreover, a method for calculating the distortion factor caused by the yield stress of different materials was proposed. Furthermore, it was demonstrated that the average effective plastic strain between the prototype and the corrected model is equal, and based on this, a similarity prediction method was established to correct the distortions caused by yield stress and the thickness of blast loaded plates. The results indicate that the proposed correction method can compensate for the differences caused by distorted factors of yield stress and thickness, with the maximum error in the structure’s peak displacement being less than 3%.

Development of Johnson-Cook-Distinct Lattice Spring Model and its application in projectile penetration into metal targets

Projectile penetration into metal targets plays an important role in modern protective structure engineering, damage assessment in terrorist attacks, and car clash accident analysis, etc. The penetration process of metal target has been characterized by large deformation, high temperature, high pressure, and dynamic damage, which can be classified as a continuous-discontinuous dynamical process. To capture the dynamic responses of metal materials subjected to high-speed penetration, Johnson-Cook model has been implemented in a continuum-discrete model, namely, Distinct Lattice Spring Model (DLSM). This is achieved by redefining the constitutive model in DLSM, with plasticity hardening (plastic strain effects), strain rate, temperature, damage evolution, equation of state, etc., being taken into account, thus developing a new numerical model called JC-DLSM model. This model is validated through studying Taylor rod high-speed impact experiments, thin metal plate penetration experiments, and projectile impact experiments on titanium alloy targets. Good agreement between numerical modelling and experimental data has been achieved for all cases considered, thereby demonstrating the capability of JC-DLSM to reproduce the damage characteristics and ballistic limits of metals under high-speed impact/penetration. Then, the impacts of projectile shape, metal target surface configuration on the characteristics of penetration damage patterns have been investigated. This contributes to a better understanding of the damage mechanisms of metal targets upon penetration or impact, facilitating the computational means for analysing and optimizing the penetration resistance of protective engineering structures.

Impact Analysis of Welding Sequence to Reduce Weld Deformation in Aluminum Hulls

Aluminum hulls, which are preferred in the marine industry due to their durability, corrosion resistance, and lightweight properties, face serious challenges due to thermal deformation during welding. This study aims to predict and minimize transverse deformations due to welding sequences for a transverse model in the lower part of an aluminum hull. To predict deformations, heat source dimensions obtained from actual weld beads were used as simulation conditions, and various welding sequence conditions were simulated through the developed finite element method (FEM). The simulation results were compared with actual deformation measurements to verify their reliability, and the optimal welding sequence which minimized deformation was derived. The simulation results show that by changing the welding sequence conditions, the maximum displacement can be reduced from a maximum of 52.1% to a minimum of 39.1%, and the effective plastic strain can be reduced from a maximum of 19.6% to a minimum of 4.8%. These results show that adjusting the welding sequence conditions can significantly improve structural integrity by minimizing deformation. The results of this study suggest that the control of the welding sequence can be used to reduce the deformation of aluminum hulls and promote a more sustainable marine industry with improved quality.

Constitutive and impact response of AA7475-T7351 under different projectile shapes and velocities: An experimental and numerical investigation

Through experimental and numerical investigation, this article investigates the constitutive and impact response of the 1.6 mm thick AA7474-T7351 plate under the impact of blunt and hemispherical-nosed projectiles at different velocities. The Johnson-Cook plasticity and failure model parameters were calibrated for the target material using experimental data from the tensile experiments, which took into consideration the effects of plastic strain, strain rate, temperature and stress triaxiality. Further, JC plasticity model parameters were also optimised using a parametric optimisation process. The flow stress of AA7475-T7351 shows positive and negative sensitivity toward loading rate and temperature. It is observed that the ductility of AA7475-T7351 decreases with increases in stress triaxiality, whereas the flow stress increases. Perforation experiments on 1.6 mm thick circular AA7475-T7351 plates were carried out using a single-stage gas gun along with the high-speed Digital Image Correlation (3D-DIC) technique. The blunt nose projectile causes shear failure, whereas hemispherical nose projectile causes combined tension-shear failure; a microscopic study is performed to confirm this phenomenon. Experimental results obtained from DIC were validated using the numerical analysis in the Abaqus/Explicit platform in terms of transient out-of-plane deformation of the target plate. The quantitative error between experimental and numerical analysis was evaluated using the Russell error technique. Numerical analysis revealed that constitutive relations could predict the physical fracture mechanisms during perforation qualitatively as well as quantitatively.

Forming quality and static properties of self-piercing riveted joints of hot-rolled steel and aluminum alloy sheets

The self-piercing riveting (SPR) Forming and tensile tests of hot-rolled steel sheet BR1200HS and aluminum alloy sheet AA 6082-T6 were simulated by Simufact Forming software. The test results show that the diameter of the rivet leg opening, which is the most important parameter affecting the mechanical properties of the joints, shows a first increase and a second decrease with the increase of rivet length, and the Max. tensile loads of the joints have the same variation law. The larger the diameter of the rivet leg opening, the greater the Max. tensile load of the joint, and the greater the effective plastic strain of the rivet of the joint. The rivet length of the joints in the five preferred SPR formation schemes obtained were all 6.5 mm, and only one scheme had a rivet hardness of H4, the rest were H5. The SPR experiment is used to verify the current finite element simulation data can get the final research conclusion. The finite element simulation (FEM) would greatly reduce the test times of the SPR test, save the test consumables and save the test cost.

Finite Element Analysis of the Mechanical Response for Cylindrical Lithium-Ion Batteries with the Double-Layer Windings

The plastic properties for the jellyroll of lithium-ion batteries showed different behavior in tension and compression, showing the yield strength in compression being several times higher than in tension. The crushable foam models were widely used to predict the mechanical responses to compressive loadings. However, since the compressive characteristic is dominant in this model, it is difficult to identify distributions of the yield strength in tension. In this study, a simplified jellyroll model consisting of double-layer windings was devised to reflect different plastic characteristics of a jellyroll, and the proposed model was applied to an 18650 cylindrical battery under compressive loading conditions. One winding adopted the crushable foam model for representing the compressive plastic behavior, and the other winding adopted the elastoplastic models for tracking the tensile plastic behavior. The material parameters in the crushable foam model were calibrated by comparing the simulated force–displacement curve with the experimental one for the case where the cell was crushed between two plates when the punch was displaced by 7 mm. A specific cut-off value (10 MPa) was assigned to a yield stress limit in the elastoplastic model. Further, the computational model was validated with two more loading cases, a cylindrical rod indentation and a spherical punch indentation, as the punch was displaced by 6.3 mm and 6.5 mm, respectively. For three loading cases, deformed configurations and plastic strain distributions were investigated by finite element analysis. It was found that the proposed model clearly provides the plastic behavior both in compression and tension. For the crush simulation, the maximum compressive stress approached 222 MPa in the middle of the jellyroll, and the maximum effective plastic strain approached 60% in the middle of the layered roll. For indentation with the cylindrical and the spherical punch, the maximum effective plastic strain approached 52% and 277% in the layered roll, respectively. The local crack or location of a short circuit could be predicted from the maximum effective plastic strain.

Serviceability limit state of incrementally launched steel bridge I-girders

Bridge girders are subjected to repeated patch loading during incremental launching (i.e. travelling over supports). Plastic deformations are likely to occur in the girder already at the first patch loading. They influence the girder’s structural response and bring about a decrease in the ultimate resistance at subsequent patch loadings. This problem is analysed in the present paper through the serviceability limit state (SLS) of incrementally launched bridge I-girders (ILBGs). The SLS of ILBGs is a current problem since only a few studies, with contrasting conclusions and certain limitations, have been recognised in the literature. Research is limited on plate girders without longitudinal stiffeners made of structural steel. Flat slide-type launching shoes are considered in this paper.The serviceability requirement (repeatable behaviour of ILBGs) and criterion (that effective membrane strains should remain in the elastic range) are adopted from the literature. So, the serviceability resistance is adopted as a load at the start of the effective membrane plastic strains in the girder. In order to propose a practical and simple SLS design procedure, the serviceability resistance is normalised against the ultimate resistance, so a serviceability correction factor (ksls) is defined. The paper presents a parametric numerical analysis of the factor (ksls). A finite element model previously developed and validated by the author is employed to simulate a nonlinear response of patch-loaded girders. The parametric study includes 599 girders. ksls is inversely proportional to the web thickness and directly proportional to the flange thickness and the yield strength of the steel material. The load length, web depth and flange width do not influence ksls. The influence of the spacing between transverse stiffeners on ksls is negligible. Finally, by regression analysis of the results of parametric study, an original and reliable serviceability correction factor is proposed as the main objective of the research. The range when the SLS of ILBGs should be checked is also defined.

Stored energy density solution for TSV-Cu structure deformation under thermal cyclic loading based on PINN

TSV-Cu is widely used for chip interconnects, where high testing costs and complex crystal plasticity finite element (CPFE) limit the research of its deep microplastic evolution process. Considering the stored energy density (SED) based on dislocation density and plastic work as a fatigue indicator factor (FIP), this paper proposes for the first time a physics-informed neural network (PINN) framework based on SED, which aims to achieve the solution of SED distributions quickly and efficiently to save computational time and cost. The grain orientation, geometrical compatibility factor, back stress, and effective plastic strain are taken into account as inputs to the PINN model. The total dislocation density is used as an indirect solution variable to construct the associated loss boundary terms, which results in the solution of the SED. The results of the two real EBSD tests show that the PINN model is able to accurately and sensitively predict the SED concentration distribution for different thermal cycle loadings, and maintains a high degree of agreement with the CPFE calculation results. Moreover, The superiority of PINN over other machine learning algorithms in terms of physical model interpretation and prediction accuracy is verified. These make it a reality for PINN to solve for the FIP distribution for the first time, and to accurately and quickly predict the location of crack initiation.

Forming limit and failure characterization of as-received and bi-axial prestrained Cu-Cr-Zr-Ti alloy sheets in the context of multistage forming

The characterization of forming limit utilizing Cu-Cr-Zr-Ti alloy sheets during the multistage forming process is imperative for successfully fabricating thrust chamber liners used in satellite launch vehicles. Therefore, the present work studies the effect of prestrain on the forming limit and failure behaviour of this alloy under different deformation paths. A stretch-forming setup was utilized to induce 8% equi-biaxial prestrain (EBP), and subsequently, these prestrained specimens were deformed till the onset of failure using the same setup. After prestraining, a shift in the failure strains was observed in the principal strain space, whereas it was found to be absent in the polar effective plastic strain, principal stress and effective plastic strain-stress triaxiality loci. The cup height along different deformation paths was marginally decreased in the prestrained specimens because of the reduction in failure strains, and the fracture occurred in the prestrained region. Further, failure analysis revealed intergranular cracks in the specimens deformed along plane strain and uniaxial deformation paths due to the presence of micron-size Cr-rich precipitates along grain boundaries. However, intergranular and transgranular cracks were present in the prestrained specimens, which were deformed equi-biaxially similar to the as-received specimens. The presence of nano-size Cr-rich precipitates inside the grains acted as nucleation sites for voids during equi-biaxial stretching, leading to transgranular cracks. It was also observed that failure in the prestrained and as-received specimens occurred at a similar effective plastic strain value due to the combined effect of void density and void size. Based on experimental observations, it was inferred that the forming limit of Cu-Cr-Zr-Ti sheets under a two-stage forming process was primarily affected by the presence of micro and nano-size Cr-rich precipitates.

The effect of elastic and plastic stresses on the electrical resistivity of conductive materials

The mobility sector has been responsible for large emissions of harmful greenhouse gases worldwide for years. E-mobility can contribute to a reduction of these emissions. For a faster spread and acceptance of electric vehicles, the achievable range and thus the efficiency of the individual components in the drive and charging train is essential. In addition to the battery and the electric machine, losses in the cables and bus bars are playing an increasingly important role. The cross-sectional shape, material and manufacturing technology of these conductive materials depends on the voltage and power to be transmitted and may still change in the future, especially in the field of fast charging and increased voltage.The aim of this work is to investigate the influence of the mechanical stress condition of copper, brass and aluminium materials on their electrical conductivity. The conductivity is measured by means of 4-wire measurements under defined tensile and compressive loads. The effects of elastic and plastic strains are taken into account. The findings can be used for an optimized manufacturing strategy for conductive components for future applications.

Fatigue crack growth in AA6082-T6/AA7050-T6 bi-materials: Effect of plastic zone ahead of crack tip

The main objective here is the understanding of the effect of plastic zone ahead of crack tip on fatigue crack growth (FCG). For that, a numerical simulation of FCG was made, based on cumulative plastic strain, considering a bi-material composed by the 6082-T6 and 7050-T6 aluminium alloys. The first one has a lower yield stress but a higher critical cumulative plastic strain. The values of da/dN are higher for the 6082-T6 which means that the effect of the easier plastic deformation dominates over the effect of the higher critical cumulative plastic strain. The bi-material 6082-7050 showed a pronounced decrease of da/dN near the interface, which starts when the monotonic plastic zone ahead of crack tip reaches the material transition. This indicates that the crack tip deformation is affected by the material inside the monotonic plastic zone. On the other hand, the bi-material 7050-6082 shows an accentuated increase of da/dN, which starts when plastic deformation is observed ahead of transition. The elimination of the contact of crack flanks reduces drastically the transient effects, which indicates that these are linked with plasticity induced crack closure effects. Crack tip blunting was proposed to be the mechanism of plasticity induced crack closure explaining the trends observed.

Shakedown of metallic sandwich beams when subjected to repeated impact loadings

When a monolithic metallic beam/plate subjected to repeated dynamic loadings with fixed impact level experiences elastoplastic deformation, its measurable deformations may cease to develop for further repetitions of the same dynamic load: this phenomenon was referred to as “pseudo-shakedown” in previous studies (Jones, 2014; Shen and Jones, 1992). Would pseudo-shakedown occur in a metallic sandwich structure under repeated shock loadings remains elusive. A combined experimental and numerical study was carried out to explore whether dynamic shakedown could occur in all-metallic ultralightweight corrugated core sandwich beams. For repeated impact tests, the sandwich beams were fabricated via the sequential process of cutting-stamping-vacuum brazing. When subjected to repeated impact loads (achieved via aluminum foam projectiles launched from a light gas gun), the dynamic responses of each sandwich specimen - including structural evolutions, beam deflections, and deformation/failure modes - were measured. Experimental results revealed that, depending upon the level of impact momentum applied to the sandwich beam, either dynamic shakedown or progressive failure could occur. The method of finite elements (FE) was subsequently employed to simulate the repeated shock tests, which was validated against experimental measurements, with good agreement achieved. To explore the physical mechanisms underlying the observed dynamic shakedown, the FE results of final plastic energy and effective plastic strain distribution in the sandwich beam were extracted and analyzed. When shakedown occurred, the measurable permanent deformation of the sandwich beam kept a relatively stable state, but its plastic energy remained positive, which is different from its monolithic beam/plate counterpart (i.e., plastic energy dropping to zero during dynamic shakedown). Such difference is mainly attributed to stress concentration occurring at the connecting joint points between the corrugated core and face sheets of sandwich and clamped endings, which produces plastic deformations that are difficult to reflect in overall large deformations of the beam. Consequently, the dynamic shakedown of metallic corrugated core sandwich beam captured in this study appears to be inexhaustive and hence may be termed as the “apparent pseudo-shakedown” (with danger lurking in the welding joints as well as clamped endings). Finally, based on a simplified bi-linear hardening constitutive law, the mechanisms underlying the dynamic shakedown of sandwich beam were further discussed from a purely base material point of view.

Numerical Analysis on the Dynamic Response of PVC Foam/Polyurea Composite Sandwich Panels under the Close Air Blast Loading.

This paper explores a novel structure aimed at enhancing its blast resistance performance by adding a layer of polyurea coating to the steel-PVC foam-steel sandwich panel. The response of 13 different arrangements of sandwich panels under explosive loading was studied using numerical simulation. The response process can be divided into three deformation stages: (1) Fluid-structure interaction; (2) Compression of the sandwich panel; (3) Dynamic structural response. The dynamic responses of the various sandwich panels to close-range air blast loading were analyzed based on the deformation characteristics, deflection, effective plastic strain, energy absorption, and pressure of the shock wave. The study draws the following conclusions: Reasonably adding a layer of polyurea to the traditional PVC foam sandwich panel can enhance its resistance to shock wave absorption, with a maximum increase of 29.8%; the optimal arrangement for explosion resistance is steel plate-PVC foam-polyurea-steel plate when the polyurea is coated on the back; and the best quality ratio between polyurea and PVC foam is 1:7 when the polyurea is coated on the front.

Elastic-Gap Free Formulation in Strain Gradient Plasticity Theory

Abstract This article presents an elastic-gap free isotropic higher-order strain gradient plasticity theory that effectively captures dissipation associated to plastic strain gradients. Unlike conventional methods that divide the higher-order stress, this theory focuses on dividing the plastic strain gradient into energetic and dissipative components. The moment stress that arises from minimizing a dissipating potential demonstrates a nonlinear evolution over time, resembling the Armstrong–Frederick nonlinear kinematic hardening rule in classical plasticity. The thermodynamically consistent framework establishes additional dissipation in the dissipation inequality. The energetic moment stress saturates as the effective plastic strain increases during plastic flow. In contrast to the Gurtin-type nonincremental model, the proposed model smoothly captures the apparent strengthening at saturation without causing a stress jump. A passivated shear layer is analytically assessed to demonstrate that the proposed theory exhibits the same amount of dissipation as the existing Gurtin-type model when they show similar shear responses at saturation. It is also shown that the plastic flow remains continuous under nonproportional loading conditions using an intermediately passivated shear layer problem. Finally, the proposed theory is validated against a recent experiment involving combined bending torsion of an L-shaped beam using a 3D finite element solution. Overall, the proposed model provides an alternative approach to evaluating the size effect within the nonincremental isotropic strain gradient plasticity theory without introducing any stress jump.

A continuum damage model for Mg/Al composite sheets rolling: Theoretical development and application

Edge cracks, which are typical formability defects, severely limit the widespread application of Mg/Al composite sheets. Accurate prediction of damage is crucial for understanding the underlying mechanisms behind crack formation. In this study, a continuum damage model that incorporates the stress-state function and effective equivalent plastic strain into the standard Lemaitre model is proposed. This enhanced model effectively addresses the issues of damage-evolution linearization and tension–compression asymmetry in the standard Lemaitre model. Thus, it can be successfully applied to predict the fracture response of ductile composite materials under pressure-forming conditions. Considering AZ31B Mg alloy and 5052 Al alloy as experimental materials, physical experiments and numerical validation are performed under a 50% reduction and 350 °C. The findings show that the proposed model effectively captures crack initiation and propagation during the rolling process, with errors of only 23.1% and 19.9% for average crack quantity and length, respectively. Results of numerical analysis reveals that the high-stress triaxiality at the edge of the sheet contributes significantly to crack formation. Additionally, the strain along the normal direction in the Al alloy significantly affects crack propagation and the formation of serrated cracks on the side of Mg alloy. This study provides important theoretical foundations for the development of Mg-based composite sheets.

Continuous damage model for structural steels and weld metals under ultra-low-cyclic loading

For the fracture problem of structural steel under strong earthquakes, a continuous damage model which comprehensively considers the influence of stress triaxiality and Lode parameter was proposed in this paper. According to the variation law of Mises stress under cyclic loading, this model decomposes the effective cumulative plastic strain into isotropic hardening and kinematic hardening components, assuming a linear proportional relationship between the fatigue damage induced by these two components. The basic mechanical properties and constitutive relationships of five common Chinese structural steels and four corresponding weld metals were investigated. The fracture failure tests for both notched round bar specimens and pure shear specimens subjected to monotonic tensile and ultra-low-cyclic loading were thoroughly examined on these materials. The continuous damage model parameters were calibrated by means of test results and complementary finite element simulations. Experimental and numerical simulation results indicate that Q690 high strength steel exhibits cyclic softening behavior, whereas the other steels show cyclic hardening characteristics. For pure shear specimens, plane strain specimens and shear energy dissipation cover plates, the continuous damage model was adopted to simulate and analyze the damage development and fracture failure process of the specimens. The predictions for crack initiation, crack propagation and fatigue life are consistent with experimental results, lending further credibility to the model. The calibrated continuous damage model of various steels provides an effective means for analyzing the ULCF fracture failure of structural steel under intense earthquakes.