Measurement Of Plastic Strain Research Articles

Investigations on the Johnson-Cook Constitutive and Damage-Fracture Model Parameters of a Q345C Steel

Due to the rapid development of high-speed trains, the service safety of vehicle body materials and structures has become a focal point in transport and impact engineering. Numerical simulations on the collision resistance of vehicle materials and structures are crucial for the safety assessment and optimal structural design of high-speed trains but have not been fully investigated due to the lack of damage model parameters. This study focuses on the Johnson-Cook (J-C) constitutive and damage-fracture models of a typical vehicle material, Q345C steel. A series of mechanical tests are conducted on the Q345C steel, including the quasi-static and dynamic compression/tension tests, quasi-static tension tests at different temperatures, and fracture tests along different stress paths, using the material test system and the split Hopkinson pressure/tension bar. Then, the parameters of the Johnson-Cook constitutive and damage-fracture models are calibrated based on the experimental results. In terms of the damage parameters related to stress paths, a new method of combining experiments and simulations is proposed to obtain the real, local fracture strains of the Q345C steel samples. This method allows the measurements of equivalent plastic strain and stress triaxiality histories under nonlinear stress paths, which are hardly accessible from individual experiments, and facilitates the accurate calibration of stress-path-related damage parameters. In addition, a high-speed plate penetration test is used to validate the J-C parameters, which can be directly implemented in the commercial finite element software Abaqus. The projectile trajectories from the simulation and experiment agree well with each other, demonstrating the reliability of the model parameters for impact scenarios and the efficiency of the experimental procedures utilized for calibration.

Tip splitting and ring formation in impact of hollow Al-6061 cylinders on Al-6061 plates

Numerous ductile failure models have been proposed in literature and it is useful to compare them for test problems. We compare three simple failure models on projectile impact problem in which hollow cylindrical Al-6061 projectiles, strike 5 mm thick Al-6061 plates at 403 m/s and undergo fracture in the projectile tip with high speed ejection of a ring-shaped fragment. High resolution simulations employing an axisymmetric formulation of smoothed particle hydrodynamics (SPH) are carried out using three different failure models: (1) a standard Johnson–Cook fit of Leuser (JC); (2) a novel Johnson–Cook fit of Ghahremaninezhad and Ravi-Chandar (GR) based upon grain-level plastic strain measurements; and (3) the Bao-Wierzbicki (BW) failure model. Numerically, the projectile tip splits and a ring is ejected when the SPH interparticle spacing 62 μm or lower, with JC or BW failure. However, simulations using JC model show further splitting of projectile tip contrary to the experiment. Grain-level GR fit produces failure of projectile tip with SPH interparticle spacing of 24 μm. This length is roughly the grain size in Al-6061. Thus, it confirms the idea of Ghahremaninezhad and Ravi-Chandar that high resolution simulations require caliberation of the failure model at the same scale. The ring dimensions obtained through simulations have a discrepancy of about 20 percent with experimental values. Hence, simple BW and GR ductile failure models reproduce experimental results in a relatively complex projectile impact. However, residual discrepancies show need for further investigation of axisymmetric SPH and failure models.

Digital-image-correlation observation of cyclic plastic strain field during the damage-accumulation mode of fatigue crack propagation under pure cyclic mode II loading for cold-rolled SUS430 steel

Fatigue cracks propagate intermittently by the cyclic initiation and coalescence of voids in front of the fatigue crack tip during fatigue crack propagation in the damage accumulation mode. In this study, digital image correlation is used to measure the evolution of the measured plastic strain distribution near the crack tip with loading and cyclic loading during one cycle. The evolution is estimated based on strain distribution measurements results and mechanical considerations. The strain is set at the unloading point because results indicate that the crack propagated in the region where the experimental shear plastic strain is the maximum in the first quarter cycle (at the first maximum load); the measured plastic strain is almost constant in the region where the crack propagates, and the crack is initiated by a subsequent cyclic strain localization and coalescence with the main crack. This study clarified the damage accumulation mode fatigue crack propagation mechanism with the measured strain behavior, and presents a method to use continuum plastic strain at the crack tip as a mechanical driving force for this mode.

State of the art methods to post-process mechanical test data to characterize the hot deformation behavior of metals

Materials engineering and science rely heavily on the indirect measurement of plastic stress and strain by post-processing of mechanical test data, including tension, torsion, and compression test. There is no consensus among researchers regarding the best test or the post-processing theory nor do adequate standards exist on the characterization methods. The tests are typically performed as customized tests, discrepancies exist in the flow curves obtained by different methods and the chosen mechanical test. More critically, the curves are dominantly treated (perceived) as a set of measured data rather than calculated values. The plasticity-based calculated flow curves and their gradients are, in turn, the basis for several second-tier indirect measurements, such as stacking fault energy and recrystallization. Such measurements are quite prone to errors due to oversimplified post-processing of the tests’ data and can only be experimentally verified in a qualitative or in an average fashion. Therefore, their findings are highly restricted by the limitations of each test, data type and post-processing method, and should be used carefully. This review examines some of the most commonly used data conversion methods and some recent developments in the field followed by recommendations. It will highlight the need to develop test rigs that can provide new data types and to provide advanced post-processing techniques for the indirect measurement.

Preisach Elasto-Plastic Model for Mild Steel Hysteretic Behavior-Experimental and Theoretical Considerations.

The Preisach model already successfully implemented for axial and bending cyclic loading is applied for modeling of the plateau problem for mild steel. It is shown that after the first cycle plateau disappears an extension of the existing Preisach model is needed. Heat dissipation and locked-in energy is calculated due to plastic deformation using the Preisach model. Theoretical results are verified by experiments performed on mild steel S275. The comparison of theoretical and experimental results is evident, showing the capability of the Presicah model in predicting behavior of structures under cyclic loading in the elastoplastic region. The purpose of this paper is to establish a theoretical background for embedded sensors like regenerated fiber Bragg gratings (RFBG) for measurement of strains and temperature in real structures. In addition, the present paper brings a theoretical base for application of nested split-ring resonator (NSRR) probes in measurements of plastic strain in real structures.

Comparative study of strength-based damage evolution in ultra-high-performance concrete (UHPC) and conventional concrete (CC) under dynamic loading

The initiation and development of damage inside cementitious materials subjected to dynamic loadings, which is manifested by the cracking and fragmentation process, have a significant contribution to the load-bearing capacity of these materials. However, current popular concrete models hypothesize that damage only initiates after the specimen reaches its peak stress, and due in part to the lack of validation from sufficient experimental data, none of the models entertain the possibility of variation in damage evolution among different types of concretes. In this study, the evolution of damage in an ultra-high-performance concrete (UHPC) and a conventional concrete (CC), characterized by the degree of strength degradation, are comparatively investigated throughout the entire pre-/post-peak deformation process as a function of carefully measured plastic strain. Well-controlled intermittent dynamic loadings are achieved on a modified Kolsky compression bar apparatus to first introduce various degrees of damage in the concrete specimens, and then the carefully preserved specimens are tested for residual strength. Coupling with pulse shaping techniques, the incident wave profiles are tailored for UHPC and CC specimens to acquire dynamic stress equilibrium and constant strain-rate deformation. Further evaluation on the residual strength of damaged specimens reveals that damage initiates prior to the peak stress, and there is a distinct difference in damage evolution between these two types of concrete materials. This investigation demonstrates a more comprehensive view of damage evolution in concrete materials and offers novel experimental data to assist the damage model development.

Measurement of plastic strain and plastic strain rate during orthogonal cutting for Ti-6Al-4V

Finite Element Modelling used to predict machining outcomes needs to be supplied with the appropriate material thermomechanical properties which are obtained by specific testing devices and methodologies. However, these tests are usually not representative of the extreme conditions achieved in machining processes and the obtained material law may not be suitable enough. Inverse identification could address this problem by obtaining material thermomechanical properties directly from machining outcomes such as cutting forces, temperatures, strain or strain rates. Nevertheless, this technique needs to be supplied with accurate machining outcomes. However, some of them such as strain or strain rate are difficult to be properly measured. The aim of this paper is to present a methodology to measure plastic strain and strain rate during orthogonal machining under plane strain conditions. The main idea is to create a physical microgrid in a workpiece and to analyze the distortion suffered by this grid. The novelty of the method consists on its capability of measuring strain and strain rate fields in a very localized area (primary shear zone) using a single image. The methodology was applied in orthogonal cutting of Ti-6Al-4V under cutting conditions that are representative of the broaching process. Experimental results were compared with DIC measurements, analytical results based on unequal division shear zone model, literature results and with numerical fields obtained from an AdvantEdge-2D model.

In-situ measurement of plastic strain in martensite matrix induced by austenite-to-martensite transformation

Employing in-situ tensile test under scanning electron microscope and micro-scale digital image correlation, the present work, for the first time, measures quantitatively the plastic strain in the martensite matrix that is induced by the martensitic transformation of retained austenite. The plastic strain is rationalized as a consequence of the large internal stresses triggered by the volume change associated with the martensitic transformation. The in-situ experimental evidence indicates that the energy barrier or the free energy change associated with martensitic transformation may need modifications to explicitly consider the associated plastic strain energy in the martensite matrix.

Phenomenological model for yield, flow, and failure behavior of dual-phase steels

We modify and extend Allain et al. (June 2015) [1]s model for dual-phase steel to obtain flow curves, global necking strains, and corresponding local plastic strain in ferrite. The model is validated by comparing with flow curves and localization strain data from the literature. Digital Image Correlation measurements of effective plastic strain on tensile specimens loaded in the SEM are used to validate our estimates of strains between martensite islands. Model predictions for steels with ferrite grain size lower than 24 μm and martensite volume fraction lower than 38%, are within 10–15% of the experimental values.

Measurement of local plastic strain during uniaxial reversed loading of nickel alloy 625

The reverse loading behaviour of polycrystalline alloys is challenging to predict, as it depends on complex multi-scale interactions that are not well understood and difficult to study. We have used high resolution digital image correlation (HRDIC) to measure the local strain development during reversed loading of a nickel based superalloy with sub-micron spatial resolution. A specially designed rig ensured that deformation remained uni-axial during reversal, and measurements were made in-situ, with the sample under load. The deformation data was correlated with the underlying crystallographic microstructure using orientation maps from electron back-scatter diffraction (EBSD), which was transformed using an affine transformation, to account for measurement related distortion. The strain was found to be localised into crystallographic slip bands separated by regions with much lower, mostly elastic, strain. On unloading, no localised deformation reversal could be measured in slip bands or elsewhere, implying that most of the strain reversal is elastic and that any plasticity during unloading is small, evenly distributed, and could not be detected using HRDIC. These results imply that HRDIC studies on unloaded samples can provide representative measurements of the deformed state of the material during reversal. On reversal, deformation is accommodated primarily by slip on slip bands formed during forward loading. In some grains, however, the slip band patterns appear to change location and sharpen with further deformation. This suggests that slip extent of slip reversal at the scale of slip bands is limited and can be quantified, opening up a new way to study reverse loading in advanced alloys.

A statistical study of the relationship between plastic strain and lattice misorientation on the surface of a deformed Ni-based superalloy

Misorientation data from Electron Backscatter Diffraction (EBSD) is often used to identify strain localisation and quantify plastic strain at the microstructural scale. However, the exact relationship between local plastic strain and misorientation and how it changes at the grain and sub-grain level has not been studied in detail. We have used high resolution digital image correlation (HRDIC) to measure plastic strain at the sub-micron scale on the surface of a nickel superalloy strained to 2%. The strain values have been correlated to different misorientation measures at the grain and subgrain scale, over several hundreds of grains. We show that although the grain mean plastic strain is positively correlated to the lattice misorientation, there is a large scatter in the correlation, which depends on the misorientation measure used. There is also essentially no correlation between the magnitude of grain strain and grain orientation derived parameters like the Schmid factor and the Taylor factor, largely due to deformation bands at the mesoscale that are not crystallographic. At these strain levels, the relationship between misorientation and plastic strain is affected by the differences in how slip (discontinuous) and lattice rotation (continuous) develop, by local grain interactions and the development of transgranular strain localisation. It is therefore effectively not possible to quantify plastic strain within individual grains using EBSD derived misorientation values alone, although some measures of misorientation are more appropriate than others if there is an understanding of the underlying local plastic phenomena. Whereas slip is localised in slip bands, the misorientation varies smoothly in a manner that is only weakly spatially correlated to the slip. These findings have implications for the modelling of the deformed state of polycrystalline metals at the microstructural scale using continuum mechanics.

Surface patterning for combined digital image correlation and electron backscatter diffraction in-situ deformation experiments

A considerable amount of information can be gained from combined collection of both digital image correlation (DIC) measurements, and of electron backscattered diffraction (EBSD) data from the same area during in-situ deformation experiments. Such data collection remains a challenge, however, due the influence of the surface markers required for DIC on the EBSD data quality. In this work we demonstrate that by careful control of the sample preparation process, a two-step electropolishing method can be used to generate excellent surface markers for DIC where the markers are integral features on the surface. The method does not require any special equipment and can be used to collect high quality EBSD data and DIC data with sub-micron resolution on the same area during repeated loading as part of in-situ deformation experiments. Combined EBSD and DIC measurements are illustrated in this work for samples of Al deformed in tension to a strain of 10%. Due to the integral nature of the surface markers we demonstrate also that it is possible to perform DIC measurements up to large plastic strains, including the necked region within a tensile sample. A comparison of EBSD and DIC data collected from the same area of a tensile-deformed sample shows that although the EBSD data provide excellent information on the lattice rotations developed during deformation, these data cannot be directly used as a measure of local plastic strain on the scale of the deformation microstructure. The ability to collect both EBSD and DIC data during an in-situ experiment provides, therefore, an opportunity to explore further the complex relationship between local plastic strain heterogeneity and EBSD-based measures of crystal lattice rotation.

Plastic Strain Threshold Determination for White Layer Formation in Hard Turning of AISI 52100 Steel Using Micro-Grid Technique and Finite Element Simulations

Abstract White layer (WL) formation in metal cutting is generally found to have negative effects on the corrosion and fatigue life of machined components. Nowadays, the mechanism of the WL formation has not been understood very well, especially about the contribution of the thermal and mechanical loadings generated by the cutting process on WL formation. The relationship between subsurface plastic strain caused by mechanical loadings and the formation of WLs is of our concern. To address this issue, WL formation in hard turning of AISI 52100 under dry and cryogenic cooling conditions is investigated by subsurface plastic strain measurement using the micro-grid technique, observed by scanning electron microscope (SEM). Due to the considerable low temperature, WL is mainly generated by the mechanical effect rather than the thermal one, and this hypothesis is supported by physically based finite element method (FEM) simulations. From the investigations, we discover the existing plastic strain threshold, which governs the occurrence of WL in hard turning of AISI 52100 steel under cryogenic cooling conditions.

Strain gradient crystal plasticity model based on generalized non-quadratic defect energy and uncoupled dissipation

The present paper proposes a flexible Gurtin-type strain gradient crystal plasticity (SGCP) model based on generalized non-quadratic defect energy and uncoupled constitutive assumption for dissipative processes. A power-law defect energy, with adjustable order-controlling index n, is proposed to provide a comprehensive investigation into the energetic length scale effects under proportional and non-proportional loading conditions. Results of this investigation reveal quite different effects of the energetic length scale, depending on the value of n and the type of loading. For n ≥ 2, regardless of the loading type, the energetic length scale has only influence on the rate of the classical kinematic hardening, as reported in several SGCP works. However, in the range of n < 2, this parameter leads to unusual nonlinear kinematic hardening effects with inflection points in the macroscopic mechanical response, resulting in an apparent increase of the yield strength under monotonic loading. More complex effects, with additional inflection points, are obtained under non-proportional loading conditions, revealing new loading history memory-like effects of the energetic length scale. Concerning dissipation, to make the dissipative effects more easily controllable, dissipative processes due to plastic strains and their gradients are assumed to be uncoupled. Separate formulations, expressed using different effective plastic strain measures, are proposed to describe such processes. Results obtained using these formulations show the great flexibility of the proposed model in controlling some major dissipative effects, such as elastic gaps. A simple way to remove these gaps under certain non-proportional loading conditions is provided. Application of the proposed uncoupled formulations to simulate the mechanical response of a sheared strip has led to accurate prediction of the plastic strain distributions, which compare very favorably with those predicted using discrete dislocation mechanics.

Elastic and Plastic Strain Measurement Using Electron Backscatter Diffraction Technique: The Influence of Sample Preparation

Elastic and Plastic Strain Measurement Using Electron Backscatter Diffraction Technique: The Influence of Sample Preparation

Tension/Compression asymmetry of a creep deformed single crystal Co-base superalloy

The creep behavior of a multinary single crystal Co-base superalloy has been compared for uniaxial tension and compression of 400 MPa applied along [001] at 850 °C. Creep under tensile stress proceeds two times faster than creep under compression. A detailed TEM study shows that already after ∼0.3 % creep strain planar faults are formed in both samples. While extended a/2<112> ribbons with SISF loops embedded in APBs are observed in tension, extrinsic SFs are revealed in compression. At ∼5 % creep strain SISFs confined to the γ′ phase dominate in tension, whereas extrinsic SFs and microtwins extending across both phases are the prevalent planar faults in compression. In addition, dense networks of regular a/2<101> matrix dislocations develop at the γ/γ′ interfaces in both loading scenarios. In tensile creep and early compressive creep the direct contribution of planar faults to plastic deformation is minor and does not exceed 10 % of the measured plastic strain. In contrast, thickening of microtwins appears to become an efficient deformation channel in the later stages of compressive creep. A pronounced asymmetry regarding the rafting kinetics is observed resulting in a P-type rafted and topologically inverted microstructure after ∼5 % creep in tension while hardly any rafting has occurred under compression. The pronounced rafting and related recovery processes are likely responsible for the inferior creep behavior in tension. Finally, two novel diffusion-assisted degradation mechanisms related to microtwins are shown to be active: an expansion of the γ phase into γ′ precipitates along microtwins and the formation of γ phase nuclei at planar fault intersections inside γ′. Both phenomena are hypothesized to be triggered by segregation of γ formers like Co and Cr to planar faults.

A new method for plastic strain measurement with Rayleigh wave polarization

In this work, a new non-contact and coupling-free ultrasound method with measuring Rayleigh wave polarization (RWP) by electromagnetic acoustic transducers (EMATs) is applied for plastic strain measurement, which can provide a very promising alternative and reference-free ultrasonic testing technique with high spatial resolution. Two specially designed EMAT receivers are developed to measure the polarization of Rayleigh wave generated by an enhanced meander-line-coil EMAT. The change in RWP due to the plastic strain has been successfully measured. And the measurement results indicate that the plastic strain at the specimen surface can be evaluated with good accuracy by measuring the relative change in RWP with the proposed EMAT-based method.

Uniaxial compression of metallurgical coke samples with progressive loading

Coke samples, produced from coals having a range of rank and vitrinite content, were subjected to uniaxial loading in a universal tester. Cokes were also imaged at high resolution using micro-CT. The aim was to understand the relationship between the internal microstructure of the coke and coke strength under load. The loading was done in two separate ways, being either compression to failure or progressive loading. The results showed that the coke samples underwent a form of stiffening at low loads, potentially due to closing of fine-scale pores and/or re-alignment of graphitic layers in the RMDC. Measurements of plastic strain indicated that these changes were permanent. At higher loads, small load-bearing components of the microstructure were found to break, leading to a softening of the coke samples. Evidence of the breaking was observed using micro-CT images before and after loading of samples. The work has relevance to the understanding of the fundamentals of coke strength, as well as to issues relating to handling and preparation of coke for standard testing.

A thermoelastoplastic theory for special Cosserat rods

A general framework is presented to model coupled thermoelastoplastic deformations in the theory of special Cosserat rods. The use of the one-dimensional form of the energy balance in conjunction with the one-dimensional entropy balance allows us to obtain an additional equation for the evolution of a temperature-like one-dimensional field variable, together with constitutive relations for this theory. Reduction to the case of thermoelasticity leads us to the well-known nonlinear theory of thermoelasticity for special Cosserat rods. Later on, additive decomposition is used to separate the thermoelastic part of the strain measures of the rod from their plastic counterparts. We then present the most general quadratic form of the Helmholtz energy per unit undeformed length for both hemitropic and transversely isotropic rods. We also propose a prototype yield criterion in terms of forces, moments, and hardening stress resultants, as well as associative flow rules for the evolution of plastic strain measures and hardening variables.

Influence of material properties and testing frequency on VHCF and HCF lives of polycrystalline copper

Predicting life times of structures, machines and their parts as well as very small electronic devices for medical purposes is especially difficult for very low stress amplitudes and very high numbers of cycles. The development of the ultrasonic-fatigue method resulted in a reliable testing technique for VHCF loading. Some of its properties are described in this paper. To offer an explanation for the somewhat controversial ultrasonic-fatigue properties reported in the literature, S-N tests were performed at ∼19kHz and 20Hz on polycrystalline copper – a nominally homogenous and ductile material. Moreover, plastic-strain measurements were performed. In addition, micro-structural features and their changes in the high and very-high cycle regimes are reported.