Plastic Material Response Research Articles

Effect of crystal orientation on the scratching behavior of γ-TiAl alloy nanowires by molecular dynamics simulation

In micro-and-nanomachining, crystal orientation effects significantly influence the plastic deformation, mechanical response, and temperature profile of nanowire materials. This study utilizes molecular dynamics simulation to investigate the process of surface scratching on γ-TiAl alloy nanowires under six different crystal orientations. The results reveal that the evolution of internal microscopic defects during the surface scratching process is heavily affected by crystal orientation, resulting in distinct dislocation motion-induced shear deformation and extrusion removal by the tool. These factors determine variations in both the shape of the nanowire's surface pile-up and the overall degree of workpiece deformation. Among all cases examined, (001)[1‾1‾0] crystal orientation exhibits easier removal of atoms with minimal internal defects, while (110)[11‾0] crystal orientation shows maximum atom removal without significant overall deformation, both cases demonstrate superior surface morphology and subsurface quality. Furthermore, stress and temperature profiles within abraded atoms and inside the workpiece depend on crystal orientation. These findings provide valuable insights for characterizing surface damage in γ-TiAl alloy nanowires as well as facilitating the preparation of surface nano-channels.

Semi-automatic miniature specimen testing method to characterize the plasticity and fracture properties of metals

Miniature-testing is essential to characterize the plastic response of materials for which the extraction of conventional full-size specimens is impossible. Examples are weld regions with high property gradients or electronic circuit components. Here, we present the design of a novel testing system for miniature specimens. After inserting the specimens with wedge-shaped shoulders, the system carries out the clamping, initial geometry scanning, and mechanical testing with digital image correlation in an automated manner. The automation prevents the accidental damaging of the miniature specimens during manual handling and adds to the robustness of the overall procedure. It is shown that the experiments with miniature specimens extracted from DP600 steel and aluminum 7075-T6 are highly reproduceable. More importantly, they lead to the same plasticity and fracture properties as experiments on conventional ten-times larger full-size specimens. A correction procedure accounting for the surface roughness, white layer and heat affect zone induced through wire EDM is provided. In addition to developing and validating the new experimental technique, it is applied to characterize a 22MnB4 rod material and stainless steel 316 L foil.

Second-order improved refined plastic hinge method with implementation of continuous strength method

Stainless steel, aluminium alloy, and cold-formed steel structures have been increasingly used as the main load-bearing components in civil engineering. However, owing to the rounded stress-strain response of the materials with significant strain hardening, the traditional plastic hinge model based on elastic-perfect plastic material response is not applicable, and the strength reduction of slender cross-sections by local buckling is also not considered. This paper proposed an improved refined plastic hinge method that can apply to different materials and fully consider the strain hardening and local buckling effect. A beam-column element was proposed, in which the second-order effect between axial load and bending moment was incorporated in the stiffness matrix formulation by using the approximate sixth-order polynomial function. The continuous strength method was introduced to the refined plastic hinge model to consider the strain hardening effect of non-slender and the local buckling effect of slender cross-sections by controlling the strength and deformability of the sections. Combining the elastic and plastic limit state criteria, the stiffness degradation function for SHS and RHS was obtained. The accuracy and efficiency of the proposed method were verified by the experimental results for stainless steel, aluminium alloy, and cold-formed steel columns of SHS and RHS under axial and eccentric compression. Finally, the proposed method was used for the design of frames for the materials, the results indicated that it was an effective tool that was ready for design practice.

Convolved action principles for couple stress elastodynamics

A novel set of variational principles and integral theorems is developed for consistent couple stress elastodynamics, including the principle of virtual convolved action, the principle of stationary convolved action, the theorem of dynamic reciprocity and the integral representation theorem. Both time-domain and Laplace-domain versions are presented. Most notably, all of these are based on the concept of convolved action, involving temporal convolutions, and are applicable to the most general case of bi-anisotropic couple stress materials. Furthermore, the principle of virtual convolved action extends beyond elastodynamics to viscoelastic and plastic material response. In addition, the two-dimensional infinite space fundamental solutions and kernel functions are derived in the Laplace-domain and used to formulate a new boundary element method (BEM) for transient response, which also originates from a convolved action. The resulting BEM is applied to four prototype examples to demonstrate the validity and robustness of the method, and to explore interesting behavior of consistent couple stress elastodynamics in the isotropic case. Although the focus here is solely on couple stress elastodynamics, the convolved action framework extends to a broad range of time-dependent problems, including those of a multiphysical nature.

PROGRESSIVE DAMAGE ANALYSIS OF STEEL-REINFORCED CONCRETE BEAMS USING HIGHER-ORDER 1D FINITE ELEMENTS

The present work investigates progressive damage in steel-reinforced concrete structures. An elastic-perfectly plastic material response is considered for the reinforcing steel constituent, while the smeared-crack approach is applied to model the nonlinear behavior of concrete. The analysis employs one-dimensional numerical models based on higher-order finite elements derived using the Carrera unified formulation (CUF). A set of numerical assessments is presented to study the mechanical response of a steel-reinforced notched concrete beam loaded in tension. The predictions are found to be in very good agreement with reference experimental observations, thereby validating the numerical approach. It is shown that CUF allows for the explicit representation of the constituents within the composite beam, resulting in accurate solutions in a computationally efficient manner.

A novel device to improve robustness of end plate beam–column connections: Analytical model development

A novel device to increase rotational capacity of steel end plate beam–column connections is proposed. By inserting a steel sleeve with a designated length, thickness and wall curvature between the end plate and the washer, the load path between the end plate and the bolts can be interrupted, promoting a more ductile response. For a specific sleeve material and dimensions, the capacity of sleeve is controlled by the amplitude value. The sleeve develops severe plastic deformations and is crushed between the end plate and the washer at the plastic amplitude. This study proposes an analytical solution to predict the plastic amplitude for the sleeve with a circular wave form. The sleeve is mathematically represented using shell of revolution theories under axisymmetric load. To simplify the analysis, the sleeve material is analysed using the two-moment limited interaction yield condition and follows an idealised rigid-perfectly plastic material response. The comparison between the proposed analytical solution with validated FE models show that the plastic amplitude is accurately captured. However, the predicted rotational capacity is very conservative.

Identification of Chaboche\u2013Lemaitre combined isotropic\u2013kinematic hardening model parameters assisted by the fuzzy logic analysis

A very good knowledge of material properties is required in the analysis of severe plastic deformation problems in which the classical material processing methods are accelerated by the application of the additional cyclic load. A general fuzzy logic-based approach is proposed for the analysis of experimental and numerical data in this paper. As an application of the fuzzy analysis, the calibration of Chaboche–Lemaitre model hardening parameters of PA6 aluminum is considered here. The experimental data obtained in a symmetrical strain-controlled cyclic tension–compression test were used to estimate the material’s hardening parameters. The numerically generated curves were compared to the experimental ones. For better fitting of numerical and experimental results, the optimization approach using the least-square method was applied. Unfortunately, commonly accepted calibration methods can provide various sets of hardening parameters. In order to choose the most reliable set, the fuzzy analysis was used. Primarily selected values of hardening parameters were assumed to be fuzzy input parameters. The error of the hysteresis loop approximation for each set was used to compute its membership function. The discrete value of this error was obtained in the defuzzification step. The correct selections of hardening parameters were verified in ratcheting and mean stress relaxation tests. The application of the fuzzy analysis has improved the convergence between experimental and numerical stress–strain curves. The fuzzy logic allows analyzing the variation of elastic–plastic material response when some imprecisions or uncertainties of input parameters are taken into consideration.

Sliding on wet sand

We present sliding experiments of a sledge on wetted sand and describe that the frictional response is controlled by the penetration hardness of the granular medium. Adding a small amount of water to sand increases the hardness which results in a decrease of the sliding friction. Pouring even more water to sand results in a decrease of the hardness and a subsequent increase of the friction. This inverse correlation between hardness of a wetted granular material and its frictional response to sliding is found to be due to ploughing of the sledge. When the load of the sledge exceeds the penetration hardness of the water-sand mixture the granular material is irreversibly deformed, which is evident by a trace of the slider left after its passage. The penetration hardness sets how deep the trace of the slider is which, in turn, controls the ploughing force. Consequently, increasing the hardness of the water-sand mixtures makes pulling a sledge over it easier. In addition, we quantify the critical shear strain which sets the transition of an elastic to plastic response of (wet) granular materials which enables us to directly relate the shear modulus, in the elastic regime, to the hardness, in the plastic regime.Graphic abstract

Elasto-Viscoplastic Material Model of a Directly-Cast Low-Carbon Steel at High Temperatures.

A model-based process control of material production processes demands realistic material models describing the local evolution of the thermal and mechanical state variables, i.e., temperature, stress, strain, or plastic strain, for the relevant microstructure state. In the present work, a material model for the specific microstructure in a continuously cast strand shell, viable for reproducing cyclic viscoplastic effects, was developed for a 0.17 wt.% C steel. Experimental data was generated using directly-cast samples and a well-controllable testing facility to apply representative loading conditions. Displacement- and force-controlled experiments in the temperature range of 700–1100 °C were conducted, with a special focus on the relevant strain rates documented for the straightening operation. A temperature-dependent constitutive material model combining elastic, plastic, and viscoplastic effects was parameterized to fit the whole set of experimentally-determined material response curves. In order to account for the cyclic plastic material response, a combination of isotropic and kinematic hardening was considered. The material model sets a new standard for the material description of a continuously cast strand shell, and it can be applied in elaborate continuous casting simulations.

The mechanics and physics of high-speed dislocations: a critical review

ABSTRACT High speed dislocations have long been identified as the dominant feature governing the plastic response of crystalline materials subjected to high strain rates, controlling deformation and failure in industrial processes such as machining, laser shock peening, punching, drilling, crashworthiness, foreign object damage, etc. Despite decades of study, the role high speed dislocations have on the materials response remains elusive. This article reviews both experimental and theoretical efforts made to address this issue in a systematic way. The lack of experimental evidence and direct observation of high speed dislocations means that most work on the matter is rooted on theory and simulations. This article offers a critical review of the competing theoretical accounts of high speed mechanisms, their underlying hypothesis, insights, and shortcomings, with particular focus on elastic continuum and atomistic levels. The article closes with an overview of the current state of the art and suggestions for key developments in future research.

The viscoelastic behaviour of material phases in fired clay identified by means of grid nanoindentation

A systematic experimental identification approach for fired clay, the base material of bricks and clay block masonry, is essential to optimize the mechanical and thermal properties and, in this way, extending the field of application of this sustainable and high-performant building material. For this reason, a comprehensive nanoindentation campaign was performed on two clays, one of them carbonate bearing, each fired at 880 °C and 1100 °C, in extrusion direction x and normal to it. A carefully defined load function, including a short preloading step, a holding phase of 20 s, and a very fast unloading step, allowed for (i) the decomposition of plastic and viscoelastic material response, (ii) the identification of the time-dependent behaviour as well as (iii) a neat determination of elastic moduli of different material phases. A well-developed sample preparation protocol, resulting in a very low surface roughness and, thus, allowing for very small indentation forces, together with the information of scanning electron microscopy images enabled the assignment of indentation responses to single material phases. An orientation dependency of the stiffness response for the matrix of both clays fired at 880 °C was identified, which, however, disappears at a firing temperature of 1100 °C. Furthermore, the indentation results revealed that every material phase within the investigated fired clay samples, even the quartz phase, has a distinct time-dependent behaviour, which could be sufficiently captured within the second loading phase of 20 s and described very well with three different rheological models. Finally, through the analysis of representative area elements of eight different fired clay samples, comprehensive 2D information about the elastic as well as viscous behaviour is given within this work, representing a basis and input for the development of micromechanical models for fired clay material.

Localization models for the plastic response of polycrystalline materials using the material knowledge systems framework

Crystal plasticity finite element simulations provide physics-based predictions of the plastic response in polycrystalline metals subjected to large plastic strains. Despite their demonstrated high fidelity in a number of applications, these approaches have not yet been adopted broadly by the metal working industry because of their extremely high computational cost. This work develops and applies a novel strategy for reduced-order partitioning of the macroscopically applied plastic stretching tensor on a polycrystalline aggregate to regions within individual grains (i.e. localization of the plastic stretching tensor). This new strategy is seen to provide reasonable predictions for the localized plastic stretching tensors at dramatically reduced computational cost. The strategy presented here extends the prior successes of the materials knowledge system (MKS) framework for the localization of the plastic stretching tensor in composites of two isotropic phases to polycrystalline volumes through the use of the generalized spherical harmonics as a Fourier basis for capturing the functional dependence of the localization kernels on the crystal lattice orientation. It is demonstrated that this extension of the MKS framework is capable of providing good predictions for all components of the second-rank local plastic stretching tensor for any given macroscale imposed plastic stretching tensor with about three to four orders of magnitude savings in the computational cost. This work has the potential to open new research avenues for computationally low-cost, fully coupled, multiscale simulations of plastic deformations in polycrystalline metals.

Cyclic Indentation of Iron: A Comparison of Experimental and Atomistic Simulations

Cyclic indentation is a technique used to characterize materials by indenting repeatedly on the same location. This technique allows information to be obtained on how the plastic material response changes under repeated loading. We explore the processes underlying this technique using a combined experimental and simulative approach. We focus on the loading–unloading hysteresis and the dependence of the hysteresis width ha,p on the cycle number. In both approaches, we obtain a power-law demonstrating ha,p with respect to the hardening exponent e. A detailed analysis of the atomistic simulation results shows that changes in the dislocation network under repeated indentation are responsible for this behavior.

Evaluation of crack growth direction criteria on mixed-mode fatigue crack growth experiments

The predictive capabilities of different fatigue crack growth direction criteria in finite element simulations are investigated. Crack growth direction criteria based on stress intensity factors, energetic measures and kinematic (displacement) measures are evaluated for mixed-mode fatigue crack growth experiments in the literature. More specifically, the development of the experimentally found crack path is simulated numerically, and the directions from the different criteria are compared to the known crack path along the development of the fracture. The simulated experiments featured proportional and non-proportional loading. Of the evaluated criteria, those based on energetic and displacement measures are able to accurately capture the tensile-mode fatigue crack growth direction for all examined experiments. Furthermore, the displacement-based criterion is able to capture the direction of shear-mode crack growth as well as the transition from shear- to tensile-mode growth and the subsequent tensile-mode growth. Modeling the cyclic elastic–plastic material response does not improve the accuracy of the predicted directions for the considered cases.

The development of a novel technique for small ring specimen tensile testing

The wide scale use of small specimens in routine testing programs could significantly reduce material resource requirements (factors of 10 are easily achievable). This is a major benefit to situations where there is not enough material to manufacture conventional, full-size specimens, such as first-stage gas turbine blade roots. However, limitations exist due to concerns over size effects, manufacturing difficulties, uncertainties related to the application of representative loading conditions and complex interpretation procedures of non-standard data. Due to these limitations, small specimen testing techniques have been mostly applied in ranking exercises and to determine approximate or simple material parameters such as Young’s modulus, minimum creep strain rate and fracture toughness. The small ring method is a novel, high sensitivity small specimen technique for creep testing that has been extended in the present work to the determination of tensile material properties. The main advantages of the small ring specimen are that it is self-aligning and has a large equivalent gauge length in comparison to other small specimens, resulting in much higher testing sensitivity. In the present work, this specimen type mimics conventional, full-size, monotonic testing, allowing for observations of elastic and plastic material response to be made. Wrought aluminium alloy 7175-T7153 small rings were tested at room temperature at 5 different loading (displacement) rates and the results compared to conventional, full-size, monotonic specimen equivalents. Finite element analysis was conducted in order to evaluate the equivalent gauge section and equivalent gauge length in the small ring specimen (which varied between circa 0.35–1.4 mm2 and 25–45 mm, respectively) to facilitate these comparisons. An analytical solution has also been derived in order to validate the finite element analysis.

On the synergy between physical and virtual sheet metal testing: calibration of anisotropic yield functions using a microstructure-based plasticity model

This paper scrutinizes in detail the synergy between physical and virtual testing of the mechanical response of sheet metal. In this context, physical testing refers to the usage of physical samples onto which mechanical tests are conducted, while virtual testing refers to multi-scale plasticity simulations onto a model representation of the metallic microstructure derived from microstructural measurement. An extensive experimental campaign was conducted to capture the plastic material response of mild steel sheet in the first quadrant of the biaxial stress space, i.e. for tensile stresses along the Rolling Direction (RD) and Transverse Direction (TD). The experimental data was acquired using state-of-the-art stress-controlled material tests enabling to probe the material up to large plastic strains in the first quadrant of stress space. Identical stress paths were simulated using the Virtual Experimentation Framework (VEF) software suite adopting the ALAMEL multi-scale plasticity model. The ALAMEL model was calibrated solely on the basis of the initial crystallographic texture of the material and a reference hardening curve obtained through a uniaxial tensile test in the rolling direction. The predictive accuracy of the ALAMEL model to reproduce the experimentally acquired material response has been thoroughly assessed. To avoid any bias in the assessment due to extrapolation of the material behavior, predictions were limited to the pre-necking regime of the material. The predictions of the VEF show good agreement with the physical test results. Subsequently, the experimental and virtual test data were used to calibrate Hill’s quadratic yield criterion and the Yld2000-2d yield function. The calibration accuracy of these yield criteria is thoroughly assessed by comparing theoretical predictions and experimental data. In addition, the calibrated yield functions are used to simulate a hydraulic bulge test and the results are compared with experimental observations. It is shown that the adopted virtual material testing procedure has reached a sufficient level of maturity to potentially serve as a viable alternative for physical material testing of steel sheet.

Modified mixed least‐squares finite element formulations for small and finite strain plasticity

SummaryIn this contribution, we propose mixed least‐squares finite element formulations for elastoplastic material behavior. The resulting two‐field formulations depending on displacements and stresses are given through the ‐norm minimization of the residuals of the first‐order system of differential equations. The residuals are the balance of momentum and the constitutive equation. The advantage of using mixed methods for an elastoplastic material description lies in the direct approximation of the stresses as an unknown variable. In addition to the standard least‐squares formulation, an extension of the least‐squares functional as well as a modified formulation is done. The modification by means of a varied first variation of the functional is necessary to guarantee a continuous weak form, which is not automatically given within the elastoplastic least‐squares approach. For the stress approximation, vector‐valued Raviart‐Thomas functions are chosen. On the other hand, standard Lagrange polynomials are taken into account for the approximation of the displacements. We consider classical J2 plasticity for a small and a large deformation model for the proposed formulations. For the description of the elastic material response, we choose for the small strain model Hooke's law and for finite deformations a hyperelastic model of Neo‐Hookean type. The underlying plastic material response is defined by an isotropic von Mises yield criterion with linear hardening.

A modified moment-fitted integration scheme for X-FEM applications with history-dependent material data

We present a strategy for the numerical integration of partial elements with the eXtended finite element method (X-FEM). The new strategy is specifically designed for problems with propagating cracks through a bulk material that exhibits inelasticity. Following a standard approach with the X-FEM, as the crack propagates new partial elements are created. We examine quadrature rules that have sufficient accuracy to calculate stiffness matrices regardless of the orientation of the crack with respect to the element. This permits the number of integration points within elements to remain constant as a crack propagates, and for state data to be easily transferred between successive discretizations. In order to maintain weights that are strictly positive, we propose an approach that blends moment-fitted weights with volume-fraction based weights. To demonstrate the efficacy of this simple approach, we present results from numerical tests and examples with both elastic and plastic material response.

Energy-based damage descriptions to assess fatigue life of steel samples undergoing various multiaxial loading spectra

The present study evaluates fatigue damage of four steel alloys, mild steel, SS347, SNCM439, and SNCM630, by means of Socie, Ellyin, and Varvani-Farahani damage models. The Socie model assesses fatigue damage through product of maximum principal strain amplitude and maximum normal stress on the maximum principal strain plane. Damage description by Ellyin was developed as both elastic and plastic strain energies over loading spectrum were integrated. The elastic–plastic response of materials is evaluated through use of Garud’s constitutive plasticity model to achieve components of stress/ strain and corresponding stress–strain hysteresis loops. Based on the Varvani-Farahani model, components of stress and strain calculated from largest Mohr’s circles over peak-valley events are employed to assess fatigue damage. Overall damage was calculated on the basis of energy-based models from counted reversals over entire loading blocks and related to fatigue life. The Socie approach overpredicted lives for steel samples. Predicted life data for mild steel and SS347 samples fell below the midline based on the Ellyin’s model. Both Ellyin and Varvani-Farahani models showed a good agreement of predicted lives for steel samples within factors ±3 as compared with experimental data. The choice of damage assessment was highly related to consistency of damage descriptions to crack formation and early growth, stress/strain components, material properties, and loading spectrum.

Effective elastic–plastic response of two-phase composite materials of aligned spheroids under uniaxial loading

In this study the incremental elastic–plastic double-inclusion model previously developed for two-phase particulate composites of spherical particles is extended to two-phase particulate composites of aligned spheroidal particles. The study is limited to the effective elastic–plastic response under uniaxial loading of composites consisting of purely elastic particles and elastic–plastic matrix of the von Mises yield criterion with isotropic strain hardening. The incremental elastic–plastic double-inclusion model is formulated through the use of the matrix tangent moduli, and evaluated by comparison of the model predictions with the exact results of the direct approach using representative volume elements containing many particles, and with available experimental results. It is shown that the incremental elastic–plastic double-inclusion formulation gives good prediction of the effective elastic–plastic response of two-phase composites of aligned spheroidal particles under uniaxial loading at moderate particle volume fractions. A unique feature of the present study is that during elastic–plastic deformation the composite matrix is treated as a two-phase material consisting of both an elastic and a plastic region.