Effect Of Strain Rate Sensitivity Research Articles

Strain rate and size effects on dynamic tensile behaviour of standard and high-strength concrete: An experimental study

The strain rate and specimen size are the main dominant factors affecting the splitting tensile behaviour of concrete. The static size effect is well-known for concrete behaviour, but it needs more knowledge about the dynamic size effect. The present study investigated the strain rate sensitivity and size effect dependency of dynamic tensile behaviour of two different grades of concretes (M35 and M60) using the Split Hopkinson Pressure Bar (SHPB) setup. From the outcomes of the experimental analysis, it was noted that the quasi-static tensile strength underwent a reduction of 8.96% and 11.39% in standard and high-strength concrete, respectively. This decrease occurred as the diameter increased from 29.5 mm to 45 mm, aligning notably with the principles outlined in the "Bazant Size Effect Law," as proposed by Bazant et al. [52]. Whereas, the dynamic tensile strength and DIF increased with increased specimen diameter, which is opposite to the quasi-static size effect. The maximum split tensile strength observed was 18.56 and 19.86 MPa, corresponding to 13.30 and 12.13 s−1 strain rates with 3.69 and 3.51 dynamic increase factor (DIF) for standard (M35) and high-strength concrete (M60), respectively. The dynamic results also demonstrated a size-effect dependency, where larger diameter specimens exhibited higher strain rate sensitivity, leading to increased strength and DIF due to lateral inertial and crack propagation effects. The modified DIF model of CEB-FIP proposed by the Malvar et al. [17] considering the strain rate and size effect simultaneously strongly supported the experimentally obtained DIF values with an ± 13% deviations. In addition, the strain rate significantly influenced the concrete failure pattern, but no size effect was observed. At a low strain rate, the initiated crack propagated towards the loading ends and split the specimen into two semi-cylindrical halves with penetration cracks. While at higher strain rates, additional wedge-shaped crushed regions formed at the loading end due to tensile and shear damage generated due to stress concentration and local crushing. The crack width becomes wider, and the triangular-shaped local crushing zone continuously moves toward the centre of the specimen from both loading ends and generates the crushed strap.

A Review on the Adiabatic Shear Banding Mechanism in Metals and Alloys Considering Microstructural Characteristics, Morphology and Fracture

The current review work studies the adiabatic shear banding (ASB) mechanism in metals and alloys, focusing on its microstructural characteristics, dominant evolution mechanisms and final fracture. An ASB reflects a thermomechanical deformation instability developed under high strain and strain rates, finally leading to dynamic fracture. An ASB initially occurs under severe shear localization, followed by a significant rise in temperature due to high strain rate adiabatic conditions. That temperature increase activates thermal softening and mechanical degradation mechanisms, reacting to strain instability and facilitating micro-voiding, which, through its coalescence, results in cracking failure. This work aims to summarize and review the critical characteristics of an ASB’s microstructure and morphology, evolution mechanisms, the propensity of materials against an ASB and fracture mechanisms in order to highlight their stage-by-stage evolution and attribute them a more consecutive behavior rather than an uncontrollable one. In that way, this study focuses on underlining some ASB aspects that remain fuzzy, allowing for further research, such as research on the interaction between thermal and damage softening regarding their contribution to ASB evolution, the conversion of strain energy to internal heat, which proved to be material-dependent instead of constant, and the strain rate sensitivity effect, which also concerns whether the temperature rise reflects a precursor or a result of ASB. Except for conventional metals and alloys like steels (low carbon, stainless, maraging, armox, ultra-high-strength steels, etc.), titanium alloys, aluminum alloys, magnesium alloys, nickel superalloys, uranium alloys, zirconium alloys and pure copper, the ASB propensity of nanocrystalline and ultrafine-grained materials, metallic-laminated composites, bulk metallic glasses and high-entropy alloys is also evaluated. Finally, the need to develop a micro-/macroscopic coupling during the thermomechanical approach to the ASB phenomenon is pointed out, highlighting the interaction between microstructural softening mechanisms and macroscopic mechanical behavior during ASB evolution and fracture.

A Multi-Yield-Surface Plasticity State-Based Peridynamics Model and its Applications to Simulations of Ice-Structure Interactions

Due to complex mesoscopic and the distinct macroscopic evolution characteristics of ice, especially for its brittle-to-ductile transition in dynamic response, it is still a challenging task to build an accurate ice constitutive model to predict ice loads during ship-ice collision. To address this, we incorporate the conventional multi-yield-surface plasticity model with the state-based peridynamics to simulate the stress and crack formation of ice under impact. Additionally, we take into account of the effects of inhomogeneous temperature distribution, strain rate, and pressure sensitivity. By doing so, we can successfully predict material failure of isotropic freshwater ice,iceberg ice, and columnar saline ice. Particularly, the proposed ice constitutive model is validated through several benchmark tests, and proved its applicability to model ice fragmentation under impacts, including drop tower tests and ballistic problems. Our results show that the proposed approach provides good computational performance to simulate ship-ice collision.

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.

Cold dwell behaviour of Ti6Al alloy: Understanding load shedding using digital image correlation and dislocation based crystal plasticity simulations

• The cold dwell behaviour of Ti6Al is analysed by a combination of digital image correlation, electron backscatter diffraction and dislocation based crystal plasticity simulations • Experiments and simulations are carried out between room temperature and 230°C to understand the worst case scenario for cold dwell and understand its physical origin • A data set of pairs of grains is analysed: some pairs of grains show the “rogue” and “non-rogue” behaviour respectively, while a novel behaviour called “non-typical rogue” is observed, in which a moderate load shedding takes place during cold dwell • The correlation between stress discontinuity at the grain boundary in “rogue” grain pairs and the distribution of geometrically necessary dislocations is analysed • The worst case scenario at 120°C is explained by the temperature dependence of the strain rate sensitivity of basal and prismatic slip systems, and the temperature dependence of the spread of geometrically necessary dislocations around the grain boundary Digital image correlation (DIC) and dislocation based crystal plasticity simulation were utilised to study cold dwell behaviour in a coarse grain Ti-6Al alloy at 3 different temperatures up to 230 °C. Strains extracted from large volume grains were measured during creep by DIC and were used to calibrate the crystal plasticity model. The values of critical resolved shear stresses (CRSS) of the two main slip systems (basal and prismatic) were determined as a function of temperature. Stress along paths across the boundaries of four grain pairs, three “rogue” grain pairs and one “non-rogue” grain pair, were determined at different temperatures. Large load shedding was observed in one of the “rogue” grain pairs, where a stress increment during the creep period was found in the “hard” grain. A minor load shedding mechanism was observed in two non-typical “rogue” grain pairs, in which the plastic deformation is nonuniform inside the grains and geometrically necessary dislocations accumulate in the centre of the grains. At elevated temperatures, 120 °C was found to be the worst case scenario as the stress difference at the grain boundaries of these four grain pairs was found to be the largest among the three temperatures analysed. The origin of this critical temperature is debated in the literature and it is investigated for the first time in the present work by analysing the simultaneous effects of the geometrically necessary dislocations (GND) and the strain rate sensitivity (SRS) of the slip systems. The analysis shows that the combined effects of the peak SRS of both prismatic and basal slip systems at 80 °C and of the increase of the spread of the GND distribution around the grain boundary at higher temperatures are the origin of the observed worst case scenario.

Non-linear dynamic finite element analysis of micro-strut lattice structures made by laser powder bed fusion

The development of additive manufacturing technologies enables the production of a new type of porous materials for the absorption of mechanical energy. These are, for example, metallic lattice structures produced by laser powder bed fusion. The structures can be made from a wide range of alloys, achieve high specific energy absorption, and can be manufactured as hybrid parts with conventional bulk components. To effectively develop lattice structures, it is necessary to complement experimental tests with simulations using the finite element method (FEM) performed under conditions of increased loading velocities. Therefore, this study focuses on the development of the FEM modelling strategy that reflects the effect of strain rate sensitivity of the base material (SS316L) and the most significant geometrical imperfections of the manufacturing process. The strain rate is reflected by the Cowper-Symonds constitutive law, which parameters are determined by the dynamic tensile test on Hopkinson split bars. The imperfections are captured by optical digitalization. The significance of the Cowper-Symonds parameters and geometric imperfections are studied independently, whereas agreement with the experiment is observed. Tests are performed for several lattice structures with different strut orientations and velocities to evaluate the versatility of the proposed approaches. A good correlation between computational and experimental results in terms of energy absorption is found for structures with an experimentally determined strut diameter and the proposed Cowper-Symonds input parameters.

Effect of Strain Rate Sensitivity on Fracture of Laminated Rings under Dynamic Compressive Loading

The effects of cladding layers of rate-sensitive materials on the ductility and fracture strain of compressed rings are numerically investigated by using the finite element method (FEM) and employing the Johnson–Cook (J–C) model. The results show that ductility is governed by the behavior of the material that is located at the ring outer wall regardless of the volume fraction of the core and clad materials. However, as the number of layers increases, this influence becomes less noticeable. Moreover, as barreling increases at the outer wall and decreases at the inner wall, fracture strain increases. Furthermore, the effects of ring shape factor and bonding type of clad and core materials are numerically evaluated. The numerical results show that less force per unit volume is required to fracture narrower rings and that using a noise diffusion pattern at the interface of the materials is more suitable to simulate crack propagation in the compressed rings and functionally graded materials (FGMs). Additionally, delamination has a direct relation to layer thickness and can occur even in the presence of perfect bonding conditions owing to differences among the material and fracture parameters of laminated layers.

In-situ investigation of dwell fatigue damage mechanism of pure Ti using digital image correlation technique

The damage behavior of soft-hard grain combinations in a pure Ti subjected to pure fatigue and dwell fatigue loading was investigated in-situ using the digital image correlation technique combined with the electron backscattering diffraction technique. The results show that the basal slip of hard grains only occurred under dwell fatigue loading, revealing that the basal slip is strongly time-dependent. The facet formation is mainly attributed to the time-dependent basal slip assisted by the locally high stress. The soft orientation also influenced the deformation degree of the hard grains under pure fatigue loading via the strain incompatibility between the soft and hard grains. These findings have significant implications in further understanding the effect of grain orientation-dependent strain rate sensitivity of the pure Ti on the dwell effect. • Dwell fatigue damage behavior of soft-hard grain combinations in a pure Ti was investigated by the digital image correlation technique. • In-situ observations demonstrate that the basal slip is strongly time-dependent. • Facet formation is mainly attributed to the time-dependent basal slip assisted by the locally high stress, related to the soft grain orientation.

Constitutive modelling for isothermal low-cycle fatigue and fatigue-creep of a martensitic steel

An improved unified viscoplastic model is developed within the framework of the Chaboche model in order to simulate the mechanical behaviour of a martensitic steel under Low-Cycle Fatigue (LCF) and Low-Cycle Fatigue-Creep (LCFC) loadings at 550 °C. The effects of strain rate sensitivity, static recovery, strain range-dependent cyclic softening, along with the effect of additional hardening under non-proportional loading are incorporated into the constitutive equations. The non-linear kinematic hardening rule is modified in such a way that it enables the simulation of the evolutionary behaviour of mean stress and the effect of decelerating stress relaxation. Finally, the prediction capability of the proposed model is illustrated for the experimental data obtained from the various strain-controlled axial-torsional tests.

An Experimental and Numerical Study of Quenching-Induced Residual Stresses Under the Effect of Dynamic Strain Aging in an IN718 Superalloy Disc

Abstract The effects of dynamic strain aging (DSA) on residual stresses generated in Ni-base superalloys during heat treatments are not well understood. In this study, the residual stress field induced by water quenching an IN718 disc while undergoing DSA is studied using coupled thermo-mechanical finite element (FE) analyses in conjunction with neutron diffraction (ND) measurements. A visco-plastic constitutive model that incorporates the effect of DSA is proposed to describe the experimentally observed negative strain rate sensitivity and abnormal temperature dependence phenomena in the stress–strain response of solid solution treated IN718. The predicted quenching residual stresses in the disc agree well with the ND measurements. Due to the DSA, a propagating high plastic strain rate region can be identified in the disc during the early stages of the quenching process. Due to the negative strain rate sensitivity and abnormal temperature dependence effects caused by DSA, the predicted residual stresses are approximately 10% greater than when those two effects are not accounted for. The effects of different convection heat transfer conditions in the FE model are examined and discussed. It is found that the convection heat transfer coefficients have a great influence both on the disc residual stresses and DSA-related plastic strain rate field predictions.

High strain rate in situ micropillar compression of a Zr-based metallic glass

High strain rate micromechanical testing can assist researchers in elucidating complex deformation mechanisms in advanced material systems. In this work, the interactions of atomic-scale chemistry and strain rate in affecting the deformation response of a Zr-based metallic glass was studied by varying the concentration of oxygen dissolved into the local structure. Compression of micropillars over six decades of strain rate uncovered a remarkable reversal of the strain rate sensitivity from negative to positive above ~ 5 s−1 due to a delocalisation of shear transformation events within the pre-yield linear regime for both samples, while a higher oxygen content was found to generally decrease the strain rate sensitivity effect. It was also identified that the shear band propagation speed increases with the actuation speed, leading to a transition in the deformation behaviour from serrated to apparent non-serrated plastic flow at ~ 5 s−1.Graphic abstract

Role of strain rate sensitivity of extrafibrillar matrix on fracture in mineralized collagen fibril arrays

Bone is a biological composite possessing complex hierarchical structure, which endows it with extraordinary damage tolerance. Despite the progress on the relationship between fracture behavior and the hierarchical structure of bone, contributions of the submicroscale constituents to fracture resistance of bone remain elusive. In this study, the calculations are carried out for fracture in staggered mineralized collagen fibril (MCF) arrays using the cohesive zone framework. The strain rate hardening of extrafibrillar matrix (EFM), post-yield strain hardening of the EFM, plastic deformation of the MCF caused by mineral/collagen sliding, and debonding of the interface between MCF and EFM are accounted for in the analyses; the individual and combined effects of strain rate sensitivity of the EFM and fracture properties of the EFM-MCF interface are revealed. It is found that for the strong EFM-MCF interface, high degree of strain rate sensitivity of EFM gives rise to low toughness of MCF arrays. Compared with plastic deformations in MCFs and EFM, interfacial debonding provides smaller contribution to toughness of MCF arrays, and plastic dissipation of MCFs is the major source of toughening. For the tough EFM-MCF interface, the toughness of MCF arrays increases with increasing degree of strain rate sensitivity of EFM, and the EFM with high degree of strain rate sensitivity promotes spreading of plastic deformation, leading to amplified damage energy dissipation in interfaces. We have further identified that strain rate sensitivity of the EFM has negligible influence on toughness of MCF arrays in the case of weak EFM-MCF interface, where interfacial debonding serves as the major toughening mechanism. However, the strain rate sensitive EFM can still activate the mechanism of spreading plastic deformation in this case, giving rise to the increase in relative contribution of plastic dissipation in MCFs with increasing strain rate sensitivity of the EFM.

Dynamic crack propagation in the turtle carapace

The turtle carapace is a biological composite shield consisting of a hard boney layer covered with a soft keratin-collagen bi-layer. The unique microstructure enables the turtle carapace to protect the underlying soft tissues from predator assaults. Recent experiments have shown that when the turtle carapace is subjected to dynamic loading, brittle fracture of the boney layer occurs, which is accompanied by delamination at the keratin-collagen and collagen-bone interfaces. To unveil the role of interfacial delamination, we propose a model of fracture in the multilayered microstructure of turtle carapace, in which brittle cracking in the boney layer, delamination of the soft bi-layer and plastic deformation in the bi-layer are taken into account. Calculations are carried out for crack propagation in the turtle carapace under dynamic loading; it is found that low strength of the keratin-collagen interface can activate large plastic deformation in the collagen layer and promote spreading of damage region in the keratin-collagen interface, which delays fracture of the boney layer. High toughness of the keratin-collagen interface increases plastic deformation in the soft bi-layer and suppresses crack propagation in the boney layer. We further reveal the role of mechanical properties of the collagen-bone interface. It is identified that high strength of the collagen-bone interface enables enhanced plastic dissipation in the soft bi-layer, retarding crack growth in the boney layer. The collagen-bone interface with high toughness plays a role in enhancing plastic deformation in the soft bi-layer, which potentially increases the resistance to crack growth in the boney layer. In addition, we explore the effect of strain rate sensitivity of the soft bi-layer. We show that decreasing the degree of strain rate sensitivity of the keratin layer can mitigate fracture of the boney layer. The findings of this study shed new light on the protection mechanisms of turtle carapace.

On the Size Effect of Strain Rate Sensitivity and Activation Volume for Face-Centered Cubic Materials: A Scaling Law

In a recent experimental study of indentation creep, the strain rate sensitivity (SRS) and activation volume v* have been noticed to be dependent on the indentation depth or loading force for face-centered cubic materials. Although several possible interpretations have been proposed, the fundamental mechanism is still not well addressed. In this work, a scaling law is proposed for the indentation depth or loading force-dependent SRS. Moreover, v* is indicated to scale with hardness H by the relation ∂ln(v*/b3)/∂lnH=−2 with the Burgers vector b. We show that this size effect of SRS and activation volume can mainly be ascribed to the evolution of geometrically necessary dislocations during the creep process. By comparing the theoretical results with different sets of reported experimental data, the proposed law is verified and a good agreement is achieved.

Effects of high Mg content and processing parameters on Portevin-Le Chatelier and negative strain rate sensitivity effects in Al–Mg alloys

Portevin-Le Chatelier (PLC) effect arises with increasing the Mg content in Al–Mg alloys. Due to the PLC effect, instability in plasticity and negative strain rate sensitivity (nSRS) are encountered during the metalworking process of the Al–Mg alloys, which reduce the ductility and formability of the materials. Herein, torsion tests are performed on the Al–Mg alloys with high Mg content to determine the effect of Mg content and processing parameters on the PLC and nSRS effects. Analyses of the flow curves and deformed microstructures reveal that the Mg content and processing parameters affect the dynamic strain aging and PLC effects in Al–Mg alloys. In some combinations of Mg content, temperature, and strain rate, the PLC effect is weakened and nSRS is not observed because the appropriate selection of Mg content and temperature can lower the stacking fault energy of Al–Mg alloy.

Size Effects of Hardness and Strain Rate Sensitivity in Amorphous Silicon Measured by Nanoindentation

In this work, dynamic mechanical properties of amorphous silicon and scale effects were investigated by the means of nanoindentation. An amorphous silicon sample was prepared by plasma-enhanced chemical vapor deposition (PECVD). Next, two sets of the samples were investigated: as-deposited and annealed in 500 °C for 1 hour. A three-sided pyramidal diamond Berkovich’s indenter was used for the nanoindentation tests. In order to determine the strain rate sensitivity (SRS), indentations with different loading rates were performed: 0.1, 1, 10, 100 mN/min. Size effects were studied by application of maximum indentation loads in the range from 1 up to 5 mN (penetrating up to approximately one-third of the amorphous layer). The value of hardness was determined by the Oliver–Pharr method. An increase of hardness with decrease of the indentation depth was observed for both samples. Furthermore, the significant dependence of hardness on the strain rate has been reported. Finally, for the annealed samples at low strain rates a characteristic “elbow” during unloading was observed on the force-indentation depth curves. It could be attributed to the transformation of (β-Sn)-Si to the PI (pressure-induced) a-Si end phase.

Strain rate sensitivity of a novel refractory high entropy alloy: Intrinsic versus extrinsic effects

In recent years, there is great interest in development of “reduced activity” refractory alloys for next generation nuclear applications for safe and efficient post-service recycling. Here, the strain rate sensitivity of a refractory high entropy alloy, namely HfTaTiVZr, was investigated consisting of all reduced activation elements. The intrinsic versus extrinsic effects in rate sensitivity were evaluated for fundamental understanding of the differences in loading condition. Uniaxial bulk and micro-pillar compression tests were performed along with multi-axial nano-indentation in a wide range of strain rates. The extrinsic strain rate sensitivity obtained from micro-pillar compression and bulk compression was higher than its intrinsic characteristic determined from nano-indentation. The low value of strain rate sensitivity obtained from nano-indentation was attributed to greater degree of dislocation entanglement in confined volume beneath the indenter. On the other hand, the high value of strain rate sensitivity in case of micro-pillar compression tests was attributed to the extrinsic effect of larger surface to volume ratio which helped in annihilation of dislocations through the free surface. A pronounced indentation size effect of strain rate sensitivity was also observed. At smaller depth, higher mobility and diffusion of dislocations near the free surface resulted in higher strain rate sensitivity compared to that at larger indentation depth.

Numerical Investigation on the Necessity of a Constant Strain Rate Condition According to Material’s Dynamic Response Behavior in the SHPB Test

The split Hopkinson pressure bar (SHPB) apparatus is frequently used to investigate the dynamic compression properties of various materials at strain rates from 102 to 104 s−1. Keeping the strain rate constant during loading is an important condition for obtaining accurate experimental results. However, we do not always need to take additional measures to control the constant strain rate loading conditions for materials with different dynamic response behaviors. To investigate the necessity of a constant strain rate condition in the SHPB test according to the different dynamic mechanical response behaviors of materials, a comprehensive numerical analysis scheme combined with the Cowper-Symonds plastic kinematic model was designed to perform the simulation tests. There are two factors primarily resulting in the errors in the calculated stress-strain response for the representative material model. One of them is the dynamic scale factor, which represents the strain rate sensitivity and controls the variation amplitude of flow stress with the change in strain rate. The other factor is the work-hardening rate, which affects the results by expanding the decrease in strain rate. This paper quantitatively describes the effects of strain rate sensitivity and the strain-hardening modulus on the accuracy of the reconstructed stress-strain behavior of a sample under a constant incident pulse. The conclusion presents several reference guides for the necessity of a constant strain rate condition for different dynamic response behaviors of materials based on the representative constitutive model.

Effect of strain rate sensitivity in visco-plastic modeling

Many crystal plasticity models use a rate sensitive law for its convenience. The rate sensitivity can be determined experimentally and input in the models. From a numerical point of view, high values of the strain rate sensitivity parameter m favor easy convergence of these models, but when m is fixed arbitrarily, which is in practice done for slightly rate sensitive materials, the physical meaning of m is lost. The present study shows that the flow stress σ, slip systems activity γs, strain anisotropy and simulated texture are strongly dependent on m. Precautions should be taken when predicting the mechanical behavior of polycrystals. To simulate nearly rate insensitive materials with models using a rate sensitive law, the use of the reference shear strain γ˙0 equal to the imposed strain rate is necessary but not sufficient. It is also necessary to use a high strain rate sensitivity parameter (m = 0.05) to correctly evaluate the material parameters, i.e., the critical resolved shear stresses (CRSS). This study also provides a relationship between the CRSS determined for different values of strain rate ɛ˙, m and γ˙0, so that CRSS determined in different studies can be compared.

Effect of Strain Rate Sensitivity and Strain Hardening Exponent of Materials on Plastic Strain Distribution and Damage Accumulation During Equal Channel Angular Pressing

Flow pattern and plastic strain distribution inside deformed sample are two important factors governing the microstructural uniformity of equal channel angular pressing (ECAP) processed materials. In the present study, the effects of strain hardening exponent (n) and strain rate sensitivity (m) on the characteristics of the ECAP process were investigated by the aid of finite element simulation. Investigated parameters are plastic strain distribution and accumulated damage. In addition, contour maps were generated to demonstrate mutual effects of n and m coefficients on the uniformity of plastic strain and maximum damage developed on ECAPed samples. Results showed that the effect of m and n values on plastic strain is more pronounced at downside regions of sample compared with upper regions. Also, at a constant strain rate sensitivity, the plastic strain is increased with decreasing strain hardening exponent due to the small corner gap formed in outer region of the intersecting area of two channels. Increasing strain rate sensitivity at constant strain hardening rate is accompanied by the formation of severely deformed area near downside of sample which leads to non-uniform strain distribution.