Strain-hardening Material Research Articles

Modeling Strain Hardening of Metallic Materials with Sigmoidal Function Considering Temperature and Strain Rate Effects.

This study uses a sigmoidal function to describe the plastic strain hardening of metallic materials, considering temperature and strain rate effects. The effectiveness of this approach is evaluated and systematically compared with other hardening laws. Incorporating temperature and strain rate effects into the parameters of this sigmoidal-type hardening law enables a more precise description and prediction of the plastic deformation of materials under different combinations of temperature and strain rate. The temperature effect is coupled using a simplified Arrhenius model, and the strain rate effect is coupled with a modified Johnson-Cook model. The sigmoidal-type hardening law is integrated with an asymmetric yield criterion to address complex behavior, such as anisotropy and strength differential effects. The calibration and validation of the constitutive model involve examining uniaxial tensile/compressive flow curves in various directions and biaxial tensile/compressive flow curves for diverse metallic alloys, proving the proposed model's broad applicability.

Tests, simulations and design of aluminium alloy equal-leg angle section stub columns after exposure to fire

This paper reports experimental and numerical studies on the compression resistances of aluminium alloy equal-leg angle section stub columns after exposure to fire. An experimental programme was first conducted, including heating tests, eight post-fire material coupon tests and sixteen post-fire stub column tests. Following the experimental programme, a numerical modelling programme was conducted, where finite-element models were developed and validated. The validated models were then used to perform parametric studies to derive additional numerical data. Based on the obtained test and numerical data, the relevant design rules used in Europe, China, America, Australia and New Zealand as well as the continuous strength method were assessed. The assessment results generally show that the current international standards lead to significant conservative and scattered design resistances when used for the post-fire design of aluminium alloy equal-leg angle sections under compression, particularly for those after exposure to elevated temperatures of 300 °C to 550 °C, due to the neglect of significant post-fire material strain hardening. The continuous strength method is found to provide greatly improved design accuracy and consistency over the European, Chinese, American and Australian/New Zealand standards for the post-fire design of aluminium alloy equal-leg angle sections, since it accounts for the post-fire material hardening.

Ductile crack growth of high-graded pipeline steels in the presence of Lüders plateau

Strain-based engineering critical assessment methods allows certain amount of plastic strain during installation and in service, for pipelines crossing seismically-active areas. Most strain-based engineering critical assessment methods are established for materials with smooth stress-strain relationship, leaving the so-called Lüders plateau influence on ductile fracture response seldomly explored. This work studied the effect of the Lüders plateau on mode I ductile crack growth with the modified boundary layer (MBL) model under plane strain conditions. The “up-down-up” constitutive model was implemented and the Gurson damage model was selected to simulate crack propagation. Factors including the plateau length and softening modulus in the “up-down-up” constitutive model, strain hardening of the matrix material and the initial void volume fraction parameter were analyzed. Numerical results show that the Lüders plateau modifies the crack tip constraint and the damage evolution, and the plateau length plays the dominant role on ductile crack growth behaviour in the presence of Lüders plateau.

Cross-process chain influence of process variations in self-piercing riveting with regard to semi-finished product dimensions

Semitubular self-piercing riveting is an important and well-established mechanical joining process. A new approach, which involves the use of high strain hardening rivet materials, has the potential advantage of increasing resource efficiency in rivet production by eliminating the normally necessary post-treatment of the rivets by means of heat treatment and coating. However, as the high strain hardening of the rivet materials leads to extraordinarily high tool loads during rivet forming, process fluctuations can be particularly critical. For example, fluctuations in the dimensions of the semi-finished products used can influence the forming process itself, but also the quality of the formed rivets, which in turn can affect the subsequent joining process and the joint formation. An increased reject rate or premature tool failure caused by this is detrimental to the resource efficiency of the entire process chain. Therefore, a fundamental knowledge of the cross-process chain cause-and-effect relationships in conjunction with fluctuating billet dimensions is needed and is acquired within this research work. The investigations show that the forming and the joining process as well as the manufactured components themselves are influenced by the billet dimensions. The forming forces and tool stresses rise with increasing billet volume. Tool failure due to excessive or uneven stress can be the result. As the billet volume increases, the head diameter and the head thickness of the rivets increase. Consequently, the joining process and the joint are also indirectly influenced by the billet volume. With increasing volume, the joining force rises and, due to the increase in the head diameter, so does the joint strength. Knowledge of the detailed relationships is therefore highly relevant for the successful use of high strain hardening rivet materials.

Development of new improved plastic collapse moment equations of pressurized different angled pipe bends under bending moments

In a piping system, pipe bends are more flexible than straight pipes because of their curved geometry, supplemented by higher stress and strain concentration, leading to one of the crucial components in piping industries. Therefore, safe design of pipe bends is essential for smooth running of the piping system, and plastic collapse moment is one of its criteria. This paper utilizes three-dimensional finite element analyses to model empirical solutions for the plastic collapse moment for different angled pipe bends subjected to combined pressure and in-plane closing, in-plane opening, and out-of-plane bending moments. Plastic collapse moments for 30∘ to 180∘ pipe bends are determined for elastic perfectly plastic and strain hardening materials, employing large geometry change option and internal pressure effect. It is observed from results that pressure effect is more prominent in thinner pipe bends of larger bend angle under all bending cases. For in-plane opening and out-of-plane bending moments, collapse moment increases and then decreases with increase in pressure intensity for all sizes of pipe bend. However, for in-plane opening bending moment, collapse moments keep on decreasing for thicker ([Formula: see text] = 11.33) pipe bends. Finally, the study presents new improved plastic collapse moment solutions for different angled pipe bends under bending moment and internal pressure, derived from the finite element results of elastic perfectly plastic and strain hardening material models.

Numerical investigation of the influence of transverse welds on the strength of aluminum alloy I-shaped members – Columns

This paper presents a numerical investigation, using finite element analysis, of the effects of transverse welds on the structural behavior of aluminum-alloy compression members. A non-linear finite element (FE) model was developed, and validated using experimental tests, to simulate the behavior of 6061-T6 aluminum-alloy columns with an I-shaped AW6×4.03 section geometry. The FE model included different material properties for the heat-affected zone (HAZ) that occurs in the proximity of the weld and the remaining base material, and incorporated both geometric and material nonlinearities. A parametric study of 80 columns with and without transverse welds was conducted, which investigated ten unbraced lengths, three weld centerline locations along the member length, and two types of post-yield material stiffness models, including elastic-perfectly plastic and strain hardening materials. The FE results provide clear evidence of the significance of the HAZ strength reduction on the load carrying capacity of welded aluminum-alloy columns. Numerical results were compared with those obtained using the provisions within the Aluminum Association’s Specification for Aluminum Structures, and they were used to develop proposed modifications to these provisions, which can remove the degree conservatism observed. A similar study on beams is presented in a companion paper.

On the Application of some Plasticity Laws

Three main rheological laws are found in the literature to describe the strain hardening of materials at high temperatures. The choice of the most suited law to describe a flow stress curve is often discussed as a function of the nature of the material; but it still remains difficult to choose the most appropriate one. These semi-empirical laws systematically comprise two main terms linked either to the dislocations generation or their annihilation.The objective of this paper is to determine by an inverse method which law appears to be the most suited. It is finally demonstrated that the application of one law is mostly equivalent to another. The various laws are overall equivalent and do not help to describe some peculiar physical mechanism of plasticity.

Effects of material strain rate, impulse profile on damage evolution of steel plates subjected to repeated pressures

This study deals with a numerical estimation of the damage evolution of steel plates used in ships and offshore structures due to repeated slamming-induced pressures. The numerical analysis model was developed using finite element ABAQUS software. Subsequently, the validated model was extended to investigate the effects of material strain rate and impulse profile on the damage evolution of plates having actual scantlings. Different strain rate models were used, and several types of impulse profiles that can be used to simplify the actual slamming pressure were adopted. In the simulation, the material strain hardening was defined for the plate model, and the impulsive pressures were applied uniformly over the plate while it was fully clamped at four edges. The results showed that a large effect of the material strain rate on the damage evolution of the plate was noticed for only several first impacts, while the effect of the impulse profile is remarkable for whole impact events. The occurrence of the pseudo-shakedown phenomenon of steel plates was examined accordingly. The results can be useful for the design of ships and offshore structures against slamming.

Effect of temperature on the plastic flow and strain hardening of direct-quenched ultra-high strength steel S960MC

This study investigates the plastic deformation and hardening behavior of the direct-quenched ultra-high strength steel S960MC at various temperatures ranging from room temperature to 900 ℃. In this regard, the Hollomon and Voce equations are used to model the hardening behavior of the material at different temperatures. The suitability of each equation to predict the plastic flow of S960MC is evaluated based on the best resulted fit for the material. In addition, microstructural investigations are carried out to indicate the correlations between the microstructural changes, occurring in the range of room temperature to 900 ℃, and hardening behavior and governing parameters. The Hollomon approach showed deviations from the experimental results for room to intermediate temperatures; however, the Voce equation modeled the material's strain hardening and flow behavior more successfully for the entire temperature range of room temperature–900 ℃. Additionally, there was a significant consistency between the Kocks-Mecking and Voce parameters. Dislocation interactions, dynamic strain aging, dynamic recrystallization, dynamic recovery, tempering (martensite decomposition), and austenite formation were the most influential microstructural features on the hardening behavior at various temperatures. The correlations between these microstructural features and hardening parameters were established satisfactorily for both the Hollomon and Voce approaches.

A shear modified GTN model based on stress degradation method for predicting ductile fracture

The Gurson–Tvergaard–Needleman (GTN) model has provided a powerful description of the nucleation growth and coalescence of micro voids, but it has limitations in simulating shear fracture due to the absence of a description of shear localization behavior. A shear improvement method is proposed for simulating the ductile fracture of materials under different stress states. The modified model not only allows for strain hardening of the matrix material, but also accounts for the stress degradation caused by shear. The strength equation of the material is described by both the shear stress state function and a decay function, making it easier for materials under shear stress state to experience material softening and further inducing shear fracture. The modified GTN model is developed by incorporating the shear stress degradation factor into the yield function, while taking into account both void growth and shear failure mechanisms. By carefully calibrating the model’s parameters, the deformation and fracture processes of tensile, plane strain, notch tensile, and compression specimens in the 7A52 aluminum alloy are simulated. The damage evolution behavior of the material under different stress states is analyzed. The results indicate that the damage include void growth mechanism and void shear mechanism. The proportions of these two mechanisms vary under different levels of stress triaxiality. Upon localizing material deformation, the shear stress state intensifies, and the shear damage mechanism assumes a critical role in fracture. The modified GTN model accurately predicts the load-displacement response and fracture path of the 7A52 aluminum alloy under a wide range of stress states.

Probabilistic-based investigation on tensile behavior of engineered cementitious composites (ECC): A macro-scale stochastic model

Micromechanics-based models are extensively used to simulate the tensile behavior of engineered cementitious composites (ECC). However, obtaining the micromechanical parameters in these models requires complicated experiments. This study proposes a macro-scale stochastic model to straightforwardly simulate the tensile behavior of ECC based on the strength criterion of strain-hardening. Specifically, the model simulates the multiple cracking of ECC as a stochastic process, in which the strength criterion is used to determine the formation of a crack. The failure probability distribution of the cracks is calculated by using statistical parameters of cracking strength and fiber bridging strength. Afterward, the crack number and tensile strain capacity of ECC are derived from the expectation of the failure probability distribution. Results show that the model predicts the crack number and tensile strain capacity of ECC with errors lower than 9.4% and 14.9%, respectively. Parametric analysis reveals that the crack number increases with the increasing difference value between cracking strength and fiber bridging strength. The stochastic model provides a comprehensive understanding on the multiple cracking of strain-hardening materials.

Strong yet strain-hardenable equiatomic CoCrFeMnNi high-entropy alloys by dynamic heterostructuring

Heterostructuring gives solutions to achieve better mechanical performance of metallic materials. For instance, partial static recrystallization by short-term annealing induces bimodal grain size distribution. Distinct from the well-studied ‘static heterostructuring’ by cold rolling followed by annealing, this study introduces ‘dynamic heterostructuring’ by hot rolling. Dynamic recrystallization (DRX) during the hot rolling as a softening mechanism leaves room for dislocation accumulation. With the expectations of enhanced strain hardening of the as-rolled materials with the aid of the DRX, we monitored tensile responses of the as-hot-rolled equiatomic CoCrFeMnNi high-entropy alloys (HEAs). Among the hot rolling temperatures from 800 ℃ to 900 ℃ with a thickness reduction ratio of 78.6% for the HEAs, the hot rolling at 850 °C results in a bimodal grain size distribution, i.e., partial DRX. It comprises relatively fine DRXed grains and coarse unrecrystallized grains: the latter is harder than the DRXed ones with relatively low dislocation density. The microstructural heterogeneity results in uniform elongation of ∼13% due to the accumulation of dislocations at the grain boundaries inside the soft DRXed grains. This endows the as-hot-rolled single-phase HEAs with strain hardenability without the aid of phase transformation, deformation twinning, or precipitates. In addition, the hot-rolled HEAs with high dislocation density have doubled yield stresses of those of conventionally cold-rolled and annealed counterparts. Considering the industrial benefits of the simplified thermo-mechanical control processes, this work extends the academic and practical value of DRX by dynamic heterostructuring through annealing-free hot rolling.

A response prediction method for clamped circular plates subjected to repeated blast loading

The aim of the present investigation is to study the behavior of metal circular plates that are clamped under the repeated blast loading at stand-off distances. In this paper, the Johnson-Cook constitutive equation involving the effects of material strain hardening and strain rate sensitivity is introduced into the empirical analysis equations used to predict the midpoint displacement of circular plates. Thus, a group of non-dimensional empirical equations are proposed for predicting the midpoint displacement of clamped metal circular plates subjected to both single and repeated blast loading. The proposed non-dimensional empirical analysis equations are verified with the simulation analysis and experimental results of previous papers. It indicates that the proposed non-dimensional midpoint displacement prediction equations demonstrate good consistency in predicting the deformation of clamped metal circular plates under both single and repeated blast loading conditions.

The macroscopic mechanical characteristics and microscopic evolution mechanism of plastic concrete

Plastic concrete has been extensively used in the underground anti-seepage engineering. Due to its complexity, there are notably discrepant between the uniaxial and triaxial mechanical behavior of plastic concrete, and the mechanism investigation on its mechanical performance remains an ongoing endeavor. In this paper, to understand the mechanical performance mechanism of plastic concrete, uniaxial tests and triaxial tests were employed to evaluate the macroscopic mechanical characteristics of plastic concrete. Moreover, the Scanning electron microscopy(SEM) and X-Ray diffraction(XRD) were utilized to probe the microstructure and composition of plastic concrete. The result of macroscopic tests showed that plastic concrete acts like strain-hardening materials and presents typical shear failure with obvious banded shear surface in higher confining pressure. The higher cement dosage and the lower bentonite content or w/c ratio increased the strength and peak strain. The E/f28 increased firstly followed by decreased with the increment of cement dosage and w/c ratio, while it increased with the addition of bentonite. As increasing the confining pressure, the strength and volume shrink deformation were enhanced while the modulus increased then decreased followed by increasing. The result of micro-test showed that the porosity of microstructure increased with the addition of bentonite and the voids of ITZ were packed up with the cementitious productions. It is suggested that the evolution of mechanical properties and microstructural features of plastic concrete are mainly driven by the synergistic effect of plasticization and solidification. The plasticization effect increased the microstructure porosity and weakened the mechanical properties of plastic concrete, while the solidification effect enhanced the bonding performance of particles in ITZ region and improved the shear strength of plastic concrete.

Molecular dynamics study on dynamic mechanical behaviour of FeCoCrCuNi high entropy alloy

ABSTRACT In this paper, molecular dynamics simulation method was used to establish the atomic model of high entropy alloy. The effect of strain rate on the microstructure evolution and dislocation motion of FeNiCoCrCu high entropy alloy was studied by applying tension and compression loads at different strain rates. The results show that the stress–strain curve of FeNiCoCrCu high entropy alloy presents three stages of elastic deformation, yield and plastic deformation under high strain rate. Under tensile load, Frank dislocation causes plastic deformation of the material, and the dislocation reaction between Shockley dislocation and Hirth dislocation generates Stair-rod dislocation. The mechanism of stress relaxation of materials under compression load is the formation of stacking faults. One of the mechanisms of strain hardening of materials is the formation of twins. In addition, stacking faults intersect with each other to produce dislocation reactions, which generate Stair-rod dislocations, maintaining the development of strain hardening effect.

An upper bound analysis of channel angular pressing process considering die geometric characteristics, friction, and material strain-hardening

In this research, an upper bound (UB) analysis of channel angular pressing process was carried out considering die geometric characteristics including die angle, thicknesses of the inlet and the outlet channels, radiuses of outer and inner corners, length of the outlet channel, as well as the length of initial billet, friction and strain-hardening of material, under cold conditions and for a billet with a rectangular cross-section. To validate the results of the UB analysis, the result of the analytical equations was compared with that of the numerical simulation and actual process. The results revealed that the total plastic strain and the process force were augmented by reducing the die angle, the outlet channel thickness, and the outer corner radius, as well as by increasing the inlet channel thickness and the inner corner radius. It was also shown that the process force increased with augmenting the initial billet length. A very good agreement was obtained between the results of the analytical method and numerical and experimental methods.

Dislocation hardening coupling between hard matrix and soft zones in a dual-phase heterostructured material

Strain hardening coupling between hard and soft zones is still not well understood in heterostructured materials. Here we report the coupling of dislocation hardening between hard iron matrix and soft copper zones in heterostructured Fe-40Cu dual-phase materials. Dislocation hardening is the predominant hardening mechanism in the Fe-40Cu materials, as dislocations dominate plastic deformation in both iron and copper. Low-temperature annealing kept highly deformed iron matrix strong and inductile but softened copper zones by promoting recrystallization in them. This raised plastic incompatibility and strain partitioning between iron matrix and copper zones during deformation. As a result, dislocations accumulated dramatically in copper zones but barely in the iron matrix. Copper zones produced high dislocation hardening to compensate for the low one of the iron matrix, raising the total strain hardening of the heterostructured Fe-40Cu materials. Lowering the plastic incompatibility between the iron matrix and copper zones weakened the strain partitioning between them and consequently depressed the dislocation hardening of copper zones. The role that copper zones played turned from producing high dislocation hardening to stabilizing the plastic deformation of heterostructured Fe-40Cu materials at the high strain level.

Mechanical performance of multi-cell thin-walled tubes under static and dynamic axial loading

In this paper, the mechanical performance of multi-cell thin-walled tubes with small aspect ratio and diameter thickness ratio and the same weight was studied theoretically, numerically and experimentally. The lightweight devices impact test was designed to get a higher velocity than the drop-weight crashing test or impacting trolley test and the experimental tests were carried out under static and dynamic axial loading. The theoretical mean crushing force (MCF) was obtained according to the simplified super folding element (SSFE) theory, and structural coefficient of the homoeomorphic structure was obtained. Then the numerical models were conducted to investigate the strain hardening on the matrix material. The results showed that the dynamic amplification factor (DAF) for the multi-cell tube to predict the MCF precisely could be ignored at or below the impact velocity 50 m/s. In addition, the experimental results indicated the initial peak forces (IPF) of the tubes were sensitive to the total length of all flanges of the cross-section. The multi-cell partitioning could improve the energy absorption of the thin-walled structures and relieve the increment of the dynamic axial loads. The energy absorption efficiency of multi-cell structure with circular tube is higher than that of multi-cell structure with square tube. The numerical model indicated the dynamic axial impact could lead to the strain hardening of the matrix material. The significant strain hardening could lead to more increment of the force.

Numerical sensitivity analysis of corroded pipes and burst pressure prediction using finite element modeling

Accurately predicting the failure pressure for corroded pipes transmitting natural resources such as oil and gas is crucial to prevent catastrophic failure and save costs. Several parameters affect the pipe's burst pressure, precisely the defective width, which is essential yet under debate. In this study, parameters such as the corrosion depth (25%, 50%, and 75%), angle (10⁰, 15⁰, 45⁰ and 90⁰), and length-to-diameter ratio “Lc/D" (0.25, 0.5, 1 and 1.5), were numerically investigated through sensitivity analysis, besides the pipes' size “D/t" ratio (16.19, 23.67, 42.64 and 79.79). The study also explored the adequacy of the previous burst pressure predicting models and proposed a new model through FE modeling. The results revealed that defect level significantly reduced the burst pressure regardless of defect angle, length, and pipe size. The defect angle ranges from 10⁰ to 45⁰, and the Lc/D ratio is less than 1, significantly impacting the burst pressure reduction for shallow and deep defects (25% and 75% wall loss). However, this impact disappears at the Lc/D ratio equals one. The findings showed that the old predictions, ASME B31G and RSTRENG, were more conservative than the newer models, DNV and Leis, for shallow defects and non-conservative for deep defects with intermediate lengths. The models that considered the material's strain hardening, such as Shaui, Leis, Ma, phan, and Netto, enhanced the predictions compared to the old ones, especially at extended corrosion. Finally, the design charts through the proposed model were generated for further adoption by codes.

Post-fire local buckling behaviour of cold-formed S700 high strength steel circular hollow sections under axial compression: Experiments, modelling and design

This paper presents experimental and numerical studies of the local buckling behaviour and compression resistances of cold-formed S700 high strength steel circular hollow sections (CHS) after exposure to elevated temperatures. The testing programme included post-fire material tests, initial local geometric imperfection measurements and stub column tests on ten specimens. Then, finite element models were developed to simulate the test structural responses and employed to perform parametric studies to generate further numerical data over a wide range of cross-section dimensions. Given that there are no existing design standards for high strength steel structures after exposure to elevated temperatures, the relevant ambient temperature design rules were evaluated, using post-fire material properties, for their applicability to cold-formed S700 high strength steel CHS after exposure to elevated temperatures, based on the test and numerical data. The evaluation results revealed that (i) the codified slenderness limits were generally accurate when used for cross-section classification of post-fire cold-formed S700 high strength steel CHS and (ii) although the codified design rules resulted in overall relatively accurate cross-section compression resistance predictions, the predicted resistances were conservative for cold-formed S700 high strength steel non-slender CHS after exposure to elevated temperatures of 900 °C and 1100 °C (owing to the high levels of material strain hardening) and those slender CHS (owing to the conservatism of the codified effective width methods).