Strain-hardening Exponent Research Articles

Development of Ca-rich slag-based ultra-high-performance fiber-reinforced geopolymer concrete (UHP-FRGC): Effect of sand-to-binder ratio

In this study, a Ca-rich slag-based Ultra-High-Performance Fiber-Reinforced Geopolymer Concrete (UHP-FRGC) with a high compressive strength of over 150 MPa and high tensile ductility (strain energy density of over 50 kJ/m3) was developed. To optimize its mechanical properties, various silica sand-to-binder (S/B) ratios ranging from 0.16 to 0.8 were considered. Geopolymeric and C(A)SH gels were produced simultaneously, and silica fume helped to increase the strength through its filler effect and accelerated the reactivity of the slag. The packing density and compressive strength of the UHP-FRGC increased with increasing S/B ratio up to 0.8, and the highest packing density and compressive strength of 0.78 and 160.7 MPa, respectively, were achieved at an S/B ratio of 0.8. Improved tensile performance of UHP-FRGC with an increase in the S/B ratio was also observed, and the best tensile performance resulted in a tensile strength of 10.3 MPa, strain capacity of 0.833%, and strain energy density of 55.0 kJ/m3. Although both the complementary energy (J’b) and crack tip toughness (Jtip) increased with the S/B ratio, the rate of increase of Jtip was much greater than that of J’b, causing a decreased pseudo strain-hardening (PSH) index. The lowest energy PSH index of 8.23 was thus obtained in the UHP-FRGC with an S/B ratio of 0.8, which provided the best tensile performance. Therefore, no correlation between the strain-hardening performance and PSH index was observed for UHP-FRGC with steel fibers.

Hot Tensile Deformation Behavior and Constitutive Models of GH3230 Superalloy Double-Sheet.

In this paper, the hot tensile deformation of a GH3230 superalloy double-sheet was conducted under deformation temperatures ranging from 1123~1273 K and strain rates ranging from 0.001~0.2 s-1. The flow behavior of the GH3230 superalloy double-sheet was analyzed in detail. The hot tensile deformation process of the GH3230 superalloy double-sheet includes four stages of elastic deformation, strain hardening, steady state and fracture. The true stress decreases with the increasing deformation temperature and decreasing strain rate. The variation of the strain rate sensitivity index and strain hardening index with processing parameters were discussed. The average apparent activation energy for hot tensile deformation is 408.53 ± 46.96 kJ·mol-1. A combined Johnson-Cook and Hensel-Spittle model considering the couple effect of strain hardening, strain rate hardening and thermal softening was established to describe the hot tensile behavior of the GH3230 alloy double-sheet. Compared to Johnson-Cook model and Hensel-Spittle model, this model has the highest predicting accuracy. The average absolute relative error of true stress between the experimental and the predicted is only 2.35%.

Study on Cyclic Bearing Capacity of Suction Pile Based on Equivalent Cyclic Creep Model

In the process of cyclic loading, strain development not only presents the strain softening phenomenon, but also a strain hardening phenomenon, depending on the different values of static deflection stress. The strain hardening and strain softening characteristics of soft clay are studied by cyclic triaxial tests. The test results show that when the static deflection stress is zero, the value of cyclic cumulative strain is small, and the strain development presents the softening phenomenon. When the static deflection stress is greater than zero, the accumulation strain increases with increasing cyclic deflection stress, and the strain development present strain hardening phenomenon. Therefore, a strain softening index and strain hardening index were proposed to describe the cyclic characteristics of soil. Moreover, an equivalent cyclic creep model was established by considering the strain hardening index to describe cyclic characteristics of suction pile. The results obtained using the proposed method are in reasonably good agreement with the measured results. This can provide a new method for analyzing the cyclic characteristics of soil and the suction pile.

Strain Hardening Exponent and Strain Rate Sensitivity Exponent of Cast AZ31B Magnesium Alloy

The flow curves of as-cast AZ31B magnesium alloy during high temperature deformation were obtained with a thermal compression test, and the effects of deformation amount, grain size, strain rate, and deformation temperature on the flow stress, strain rate sensitivity index, and strain hardening index were analyzed. The results showed that deformation and grain size were negatively correlated with both the strain rate sensitivity index and strain hardening index. The increase in strain rate increased the strain hardening index but made the strain rate sensitivity index show an opposite trend. Increasing temperature reduced the strain rate sensitivity index and strain hardening index but, when the temperature exceeded 700 K, the strain rate sensitivity index was no longer affected by temperature. Since the strain rate sensitivity index m and strain hardening index n are important parameters for measuring the plastic deformation of metal materials, this study has great significance for guiding the selection of process parameters in the plastic processing of as-cast AZ31 magnesium alloy.

Role of synergistic hardening and damage evolution on the stretchability of Al1050/steel/Al1050 sheets

The configurational design of heterostructures has received considerable attention to achieve a superior combination of strength and ductility. Although heterostructuring for enhanced tensile properties has been widely analyzed, studies on the effect of heterogeneity on sheet formability are still insufficient. Sheet metal formability is one of the most crucial factors for determining hetero-materials’ industrial utilization. To broaden the industrial applicability of heterostructured layered materials, investigating the effects of heterogeneity in the layered structure on formability is necessary. This study investigated the stretch formability of aluminum-steel-aluminum clad sheets using the Erichsen cupping test. The three-layered clad sheets showed additional hardening with a slight increase in ductility owing to hetero-deformation-induced hardening because the strain-hardening exponent has a linear relationship with stretchability or necking resistance. After necking, damage evolution owing to severe internal stress concentration led to delamination at the interface. Interestingly, delamination serves as a block to full cracking through the thickness during forming. This study contributes to the industrial applicability of heterogeneous structuring by elucidating the characteristics of heterogeneity and formability.

Extraction of the plastic properties of metallic materials from scratch tests using deep learning

Powered by machine learning and computer technology, neural networks have opened new paths for solving engineering problems. In this paper, the plastic parameters, i.e., the yield stress and strain hardening index, of metallic materials are extracted from scratch tests using deep learning methods. Using a dataset generated by finite element simulations, three network models, i.e., the classical multi-output multi-layer perceptron (MLP), a single-target approach (ST-MLP) and the parameter sharing-based deep network (DMTR), are adopted to determine the relationship between scratch responses and plastic parameters. According to the test dataset results, the DMTR performs better than the MLP and ST-MLP. The trained DMTR is verified by comparing the plastic parameters of 18CrNiMo7-6 alloy steel, 304 stainless steel, and brass obtained from scratch tests with those under tension. This work is expected to provide an alternative method for determining the plastic parameters of metallic materials.

Determination of plastic properties of surface modification layer of metallic materials from scratch tests

A new test method was proposed to extract plastic parameters, i.e., yield stress and strain hardening index, and interfacial coefficient of friction of metallic materials via scratch tests with a pyramid indenter based on dimensional analysis and finite element analysis. Yield stress and strain hardening index of scratched materials can be calculated with scratch width, residual scratch depth and normal force obtained from the scratch tests. Interfacial coefficient of friction between the scratched materials and scratch tip can be determined by the ratio of tangential force and normal force. The accuracies of the proposed formulas were verified by comparing the results of uncarburized and carburized 18CrNiMo7-6 alloy steel obtained by conventional methods with those by scratch tests. This work provides a convenient method to determine plastic parameters and interfacial coefficient of friction of metallic materials simultaneously, which is important for the mechanical analysis, design and safety evaluation of mechanical parts.

An Incremental Contact Model for Rough Surfaces of Strain-Hardening Solids

The load–area relation of rough surfaces is of great interest in tribology. For elastic–plastic solids with strain hardening, an incremental model is adopted to analyze the contact of rough surfaces, in which the contact is modeled by accumulation of equivalent circular contacts with varying radius. For three typical rough surfaces with various material properties, comparisons with direct finite element calculations demonstrate the efficiency of this incremental contact model. An approximate linear relation between load and contact area is predicted by both methods up to a contact fraction of 15%. The influence of yield stress and strain-hardening exponent on the load-area proportionality is presented. This work gives a simple while effective method to calculate the load-area relation for rough contact of strain-hardening materials.

Two-parameter elastic-plastic fracture criterion and corrected fracture toughness

The basic aspects of the J-A concept of elastic-plastic two-parameter fracture mechanics, based on a three-term asymptotic description of the stress field at the crack tip are presented. It is noted that the field of elastic-plastic stresses at the crack tip is controlled by two parameters of fracture mechanics, namely, J-integral and parameter A. Parameter A is a measure of the deviation of the stress field from the HRR-stress field and can be considered a parameter of elastic-plastic constraint at the crack tip both under conditions of small- and large-scale yielding. The results of studying the influence of the exponent of the strain hardening of the material, crack aspect ratio and the thickness of standard specimens with a crack on the elastic-plastic stress intensity factor and parameter A are presented. A two-parameter elastic-plastic J-A fracture criterion based on the relationship between J-integral and strain(stress) on the surface of the crack-notch and the principle of linear summation of damage is formulated. To reflect the crack-tip constraint, the parameter A is introduced into the criterion equation as a function of applied failure stresses. The elastic-plastic fracture toughness as a function of the crack-tip constraint in the fracture criterion is interpreted as the corrected elastic-plastic fracture toughness of a specimen with the corresponding constraint parameters A. The results of studying the normalized corrected fracture toughness as a function of failure stresses, crack aspect ratio and strain hardening exponent of the material are presented.

A constitutive model for the uniaxial tensile plastic behavior of metals based on the instantaneous strain-hardening exponent

The present work develops a new constitutive equation model for strain-hardening behavior of metallic materials (named herein as the Gonoring model) based on the definition of the instantaneous strain-hardening exponent. This new proposal was applied to experimental uniaxial tensile data of a lean duplex stainless steel alloy UNS s32304 (LDSS 2304) in the as-received (AR) condition and on identical heat-treated specimens at four different temperatures. This choice was justified because this is a steel that presents two phases (ferrite and austenite), which makes it a more universal example from the point of view of applying a new constitutive equation model. These heat treatments induced sigmoidal strain-hardening behavior at uniaxial tensile in this alloy. The Gonoring proposal was able to predict the strain-hardening behavior of both the sigmoidal and parabolic-shaped strain-hardening curve of a lean duplex stainless steel alloy 2304.

Solutions and applications of 3D elastic–plastic constraint parameters for clamped single edge notched tension (SENT) specimens

Single edge notched tension (SENT) specimen is a common fracture toughness test specimen now widely used in the pipeline and pressure vessels industries. In this paper, an extensive study has been conducted by three-dimensional (3D) finite element analyses (FEAs) to investigate the in-plane constraint parameters (namely A and QSSY) and out-of-plane constraint parameter, that is, Eε33 for clamped SENT specimens with side-grooves. A wide range of crack depth to specimen width ratios a/W = 0.2, 0.3, 0.4, 0.5, 0.6 and 0.7, specimen thickness to specimen width ratios B/W = 0.5, 1.0, 1.5, 2.0, 3.0 and 4.0 were included. The various strain hardening exponent (n = 4, 7, 10) and applied loading levels (from small-scale yielding to large-scale yielding) were also investigated. The results show that the effects of crack depth, specimen thickness, loading level and strain hardening index on the 3D constraint parameters show a significant coupling effect. With the increase of load level, A value increases monotonically, while QSSY and the normalized Eε33 (called V33) decrease, and the influence of specimen geometry on the constraint levels will become greater. The values of A and V33 obviously decrease with the increase of hardening exponent, but the change of QSSY is relatively small. Moreover, it can be observed that both A and QSSY can well describe the in-plane constraint effect, and V33 can better quantify the out-of-plane constraint effect under varying loading levels and n. In addition, elastic–plastic constraint parameters were also calculated for various experimental test specimens made of 16MND5 steel, with n = 9.2. It was demonstrated these constraint parameters can be applied to quantify and predict the J-R curves of 16MND5 steel with good agreements for specimens with different in-plane and out-of-plane constraint conditions.

Data-Driven Derivation of Sheet Metal Properties Gained from Punching Forces Using an Artificial Neural Network

The ongoing digitization of production processes provides new possibilities and potentials for process monitoring of forming and stamping processes. The component quality achievable by these processes is strongly dependent on the properties of the sheet metal material, so that a permanent digital recording of material data offers high potential for monitoring each component produced. In this context, presented paper deals with a novel AI-based method for the direct determination of ma-terial parameters from measured punching force curves. Using software systems Python and Tensor-Flow, an artificial neural network was first set up to determine mechanical material parameters (out-put data) from punching force curves (input data). As data basis for the adopted neural network, force curves were measured during punching of various sheet metal materials using a punching tool equipped with a direct force measurement device. Punching force curves were experimentally deter-mined for the sheet metal materials DP1200, DP1000, DP800, DP600, HX380LA, DC03 and DX54. Additionally, tensile tests were performed for these sheet metal materials to determine ultimate tensile strengths (Rm), yield strengths (Rp0.2, Re), uniform strains (Ag), elongations at break (At) and strain hardening exponents (n). The presented paper reveals that neural networks can accurately quantify the relationship between characteristic parameters of punching force curves and the mentioned me-chanical material properties.

Study on the Properties of Fiber/Matrix Interface and Strain-Hardening Behavior of ECC Containing Municipal Solid Waste Incineration (MSWI) Powder.

In this paper, the mechanical properties of micropowder cement mortar and engineered cementitious composites (ECC), using different processing municipal solid waste incineration (MSWI) as a mineral admixture, were investigated. Through the direct ball milling method, ball milling heat treatment method, water washing ball milling method and water washing heat treatment ball milling method, the mechanical properties of MSWI bottom slag-regenerated micropowder cement mortar were tested. Compared with other groups, the flexural strength and compressive strength of the specimen prepared by the MSWI after washing and heating (750 °C, 5 h) were the highest, which reached 82.0% and 81.0% of the reference group, respectively. Based on this treatment, a uniaxial tensile test, three-point bending test and single fiber pull-out test were then carried out to explore the relevant ECC properties containing MSWI. The strain-hardening index PSH of ECC was determined by analyzing the fracture toughness and elastic modulus, fiber/matrix interface chemical bond and friction bond strength of ECC containing MSWI. The results showed that the PSH index of ECC was higher when the treated powder content was 2.2, the w/c ratio was 0.25 and the fiber volume content was 2.0%. This led to higher tensile ductility, which made it easier to achieve stable multi-slit cracking and strain-hardening behavior.

Flexural buckling of extruded high-strength aluminium alloy SHS columns

The structural performance and design of extruded high-strength aluminium alloy square hollow section (SHS) columns were presented in this paper. A total of 12 extruded 7A04-T6 aluminium alloy SHS column specimens were tested under axial compression, together with tensile coupon tests and initial global geometric imperfection measurements. The flexural buckling failure mode and axial load versus end shortening and mid-height lateral deflection curves were reported. Based on validated finite element (FE) models, 480 numerical results were generated by means of parametric studies over a broad range of cross-section dimensions, member lengths, proof strengths and strain hardening exponents of the aluminium alloy material. The applicability of current design rules used for normal-strength aluminium alloy columns in European, Chinese and American standards to extruded 7A04-T6 high-strength aluminium alloy SHS columns was evaluated through comparisons with the test and FE results. The analysis results showed that the three standards consistently yielded conservative axial compression resistance predictions by about 9% for extruded 7A04-T6 high-strength aluminium alloy SHS columns. New flexural buckling curves with linear and nonlinear imperfection terms for the Chinese code, as well as modifications to the American specification, were separately proposed, resulting in improved accuracy with significantly reduced scatter. Additionally, the continuous strength method (CSM) was further extended for the flexural buckling design of extruded 7A04-T6 high-strength aluminium alloy SHS columns, and was shown to provide accurate and consistent resistance predictions. Reliability analyses of the codified and the proposed design methods were performed, confirming that the design proposals meet the target reliability indices except the Eurocode approach.

On the application of the forming limit diagrams for quality control of blanks for wheelbarrow of ASTM A1008 carbon steel

The effectivity of the forming limit diagrams in manufacturing wheelbarrow by deep-drawing is shown because of the high material scrap rate which reduces productivity. Several chemical, mechanical testing and microstructural analysis were performed to examine sheet quality and their impact on these diagrams. Chemical analysis revealed that Steel 1 and Steel 3 sheets fulfilled the specification without assuring adequate forming process. However, the higher titanium content of Steel 2 improved its formability since it promoted the formation of fine precipitates, thus refining the grain size. This steel had the highest ASTM grain size number G (9.11), which is the lowest average grain size (13 µm) compared to the other steels, which had G values in the range 8.7 to 9.11. Moreover, Steel 2 sheets had the greatest plastic strain ratio (rm = 1.80), the highest strain-hardening exponent (n = 0.250), the lowest anisotropy ∆r = 0.31), yielding better results in deep-drawing strain distribution, the highest forming limit strain (28%) and the highest uniform elongation zone, favoring that failure sites did not occur.

Effects of geometric array and size of internal voids on tensile ductility of AZ31 magnesium alloy sheets

This study aims to investigate the contributions of the geometric array and size distribution of perforated cylindrical voids to the tensile strain of a metallic sheet through the numerical correction of the plastic constraint factor with regard to the geometric array of internal voids. In AZ31 alloy sheets fabricated via strip casting, internal voids were formed via mechanical drilling in the form of perforated cylindrical holes. The tensile strain decreased significantly (from 0.18 to 0.01) as the void area fraction increased to 40%, and its nominal value decreased with an increase in the void size, even when the geometric array (ratio of void size to ligament distance between voids, a/l) was maintained. A plastic constraint factor describing the geometric array and size distribution of perforated cylindrical voids was proposed through the modification of an original form for isolated spherical voids, and the theoretical prediction using a modified constitutive model agreed well with the experimental results. The tensile ductility of a metallic sheet with perforated cylindrical voids depends more sensitively than isolated spherical voids on the variation in the void area fraction, because the effective void area fraction is overestimated by the exclusion of the strain-hardening exponent term in the modified plastic constraint factor. Additionally, increases in the void size and void area fraction at a fixed a/l ratio lead to a reduction in the tensile strain, by the increase of the plastic zone and the intensification of stress concentration around a void.

Simultaneous improvement of strength and ductility by Mn addition in extruded Mg–Gd–Zn alloy

The influence of Mn content on the microstructure, tensile properties and strain-hardening behaviors of extruded Mg−1Gd−0.5Zn−xMn (x=0, 0.3 and 1, wt.%) alloy sheets was investigated by X-ray diffraction (XRD), scanning electron microscope (SEM), and electron backscatter diffraction (EBSD). The results show that the completely recrystallized grain structure and the extrusion direction (ED)-titling texture are observed in all the extruded sheets. The mean grain size and weakened ED-titling texture of the extruded sheets are gradually reduced with increasing Mn content. This is primarily associated with the formation of new fine α-Mn particles by Mn addition. Tensile properties show that the addition of Mn also leads to the improvement of yield strengths, ultimate tensile strengths and elongations of the extruded Mg−1Gd−0.5Zn−xMn sheets, which is mainly due to the fine grains and α-Mn particles. In addition, the Mg−1Gd−0.5Zn−1Mn sheet has the lowest strain-hardening exponent and the best hardening capacity among all prepared Mg−1Gd−0.5Zn−xMn sheets.

Improvement of stretch formability and weakening the basal texture of Mg alloy by corrugated wide limit alignment and annealing process

In this paper, a process of corrugated wide limit alignment (CWLA) was used to improve the stretch formability of large-dimension AZ31 Mg alloy sheets by inducing tensile twins. The effects of {10 1¯ 2} tensile twins on microstructure evolution, mechanical properties and stretch formability of AZ31 Mg alloy sheet was studied. The results indicated that the CWLA samples exhibited a weakened basal texture and a high fraction of twin boundaries due to the twinning and recrystallization behavior. After CWLA and annealing for 30min at 300 °C, the strain-hardening exponent value increased from 0.2 to 9.4, the Lankford value decreased from 2.85 to 0.37, and the Erishen value was increased by ∼95% compared to the as-received samples. The present study would provide a new insight into the development of Mg alloys having excellent stretch formability.

A review on the reverse analysis for the extraction of mechanical properties using instrumented Vickers indentation

Abstract This work presents a review on recent methodologies for the analysis of data obtained through instrumented indentation testing. Experimental tests, using a Vickers indenter, were carried out on low-carbon and bearing steels and indents were later analyzed in a laser interferometer. The results were used to verify the accuracy of methods proposed to predict the indentation morphology, pile-up or sink-in, and the accuracy of routines proposed to extract the mechanical properties of the indented materials. The occurrence of pile-up in all tested materials indicated that models may fail in predicting this behavior and, consequently, in determining the yield stress and strain-hardening exponent.

Anisotropic elastic–plastic properties of surface-modified layers of 18CrNiMo7-6 alloy steel after carburizing heat treatment determined by an indentation method

This work considers the analytical solution of the contact problem between a conical indenter and a transversely isotropic material, and uses a finite element method to determine the correction coefficient to implement in the analytical solution involving a Vickers indenter. Meanwhile, an indentation characterization method was established to determine the elastic modulus of the transversely isotropic material. By applying the finite element model of indentation to evaluate transversely isotropic materials, the dimensionless functions used to compute the yield strength, strain-hardening exponent, and yield strength ratio could be established based on the sensitivity analysis of the plastic parameters. The anisotropic elastic–plastic properties of surface-modified layers (SMLs) were characterized by treating the SML as several layers of transversely isotropic material. Indentation tests were carried out to study the SMLs at different depths, and their elastic–plastic parameters were obtained using the proposed method. The results indicate that the elastic modulus in the longitudinal direction and the isotropic plane at the same depth are distinct, and there is a small difference between the yield strengths in the longitudinal and vertical directions of the heat-treated 18CrNiMo7-6 alloy steel. However, the yield strength ratios in both directions are generally constant along the depth of the SML. As the depth of the SML increases, the yield strength and hardening index also decrease gradually.