Strain Rate Dependence Of Strength Research Articles

Multiscale Richtmyer-Meshkov instability experiments to isolate the strain rate dependence of strength.

Theoretical analysis of Richtmyer-Meshkov instability (RMI) experiments for solid strength shows that the strain rate for a given shock should be inversely proportional to the length scale of the sine wave perturbations when η_{0}k, the nondimensional amplitude to wavelength ratio, is held fixed. To isolate the effect of strain rate on strength, free-surface RMI specimens of annealed copper were prepared with three perturbation regions with the same η_{0}k but different length scales, characterized by the wavelength λ varying by a factor of 4.9 from 65 to 130 to 320µm. Three such targets with different fixed η_{0}k^{'}s were impacted to a shock pressure of 25 GPa, and the instability evolution was measured with photon Doppler velocimetry. Strengths estimated by comparing hydrocode simulation to the data increased from 700 to 1200 MPa as λ decreased. The different η_{0}k targets exercised increasing amounts of plastic strain yet showed no evidence of strain hardening. Physical regime sensitivity analysis determined that for 320-65µm wavelength perturbations, the effective strain rates increased from 8.7×10^{6} to 3.3×10^{7}s^{-1}, a factor of 3.8. Thus, the predicted strain rate scaling was mostly achieved but slightly suppressed by increased strength at higher rates. The RMI strength estimates were plotted against constitutive testing data on copper from the literature to show striking evidence of the strength upturn at higher strain rates.

Establishing a data-driven strength model for [formula omitted]-tin by performing symbolic regression using genetic programming

Tin (Sn) exhibits complex deformation behavior characterized by significant dependence of strength on temperature and strain rate. This work develops a strength model for tin by using genetic programming to perform symbolic regression on a set of compression tests at various strain rates and temperatures. The strength model developed in this work showed increased accuracy compared to traditional strength models. Furthermore, the developed strength model adequately predicted independent experimental data (i.e., data that was not used to train the model). Results demonstrate that genetic programming successfully established a valid analytical function that adequately characterizes the temperature and strain rate dependent strength behavior of tin. Therefore, demonstrating that the developed framework provides robust and accurate formulations of strength models.

Microstructure evolution and compressive properties of a low carbon-low alloy steel processed by warm rolling and subsequent annealing

A low carbon-low alloy steel was processed by warm rolling with reductions range from ~30% to ~70% followed by annealing at 450°C. Then, the microstructural evolution was characterized by Field Emission Scanning Electron Microscopy (FE-SEM), Electron Backscatter Diffraction (EBSD), Transmission Electron Microscopy (TEM), X-ray Diffraction (XRD) and compressive testing under strain rates of 1.0 × 10−3–2.0 × 103 s−1 was carried out. Microscopy analyses showed that ultrafine-grained structures with high-density dislocations and more and finer M3C carbides by comparison with the tempered steel were achieved after warm rolling. Subsequent annealing promoted the further precipitation of finer carbides and led to dislocation recovery as well as a slight coarsening of grains. Compressive testing results indicated that the yield strengths of the warm rolled steels at different strain rates were significantly increased by ~40–70% compared with the as-received sample, which was mainly attributed to a combination of dislocation strengthening, grain boundary strengthening and precipitation strengthening. After annealing, the yield strength decreased slightly due to a dislocation recovery and a slight increment of the grain sizes. In addition, the influence of microstructure evolutions including dislocation densities, grain sizes and carbide precipitations during warm rolling and subsequent annealing on the strain rate dependence of strength for steels was also analyzed.

Influence of strain-rate related parameters on the simulation of ballistic impact in woven composites

The mechanical behaviour of strain-rate-dependent materials varies when they are exposed to dynamic conditions (compared with static ones), and material parameters like modulus, strength, and failure strain may depend on the loading rate. Simulation of the ballistic impact effect on composite materials may be strongly dependant on the suitable calibration of the strain rate effect on their constitutive law. Indeed, knowledge of the strain rate-dependent properties is of great interest but still lacks comprehensive studies (i.e., the effect on the mechanical parameters, besides strength, is commonly ignored). In the present work, three meso-heterogeneous models for 2D woven glass-fibre composites under impact loading were built considering strain rate-dependent strength, modulus and failure strain, coupled with macro-homogeneous models with and without the strain rate effect on strength. All the numerical predictions were compared with actual ballistic test results. It was found that the accuracy in residual velocity and damage morphology predictions can be improved by considering the strain rate effect on modulus and failure strain.

Effect of Strain Rate on Compressive Properties of High-Speed Tool Steel

In the present study, the effect of strain rate on compressive properties of high-speed tool steel was experimentally investigated. It is not easy to obtain the stress-strain relationship under high-speed deformation since high-speed tool steel has very high strength. In order to carry out the impact compressive test of high-strength materials, we developed the split Hopkinson bar (SHB) compression test apparatus using cemented carbide for the elastic bar. The impact test was obtained at the strain rate of 103 s-1. The quasi-static test was carried out at strain rates of 10-3 to 10-1 s-1. Both tests were conducted under three temperature conditions, 298 K, 201 K, and 77 K. Within the set of experiments, almost all specimens showed an increase in flow stress with increasing strain rate (strain rate dependence of material strength) was confirmed. However, the impact test at 77 K showed that the effect of work softening was greater than the strain rate dependence of strength.

An improved material model for loading-path and strain-rate dependent strength of impacted soda-lime glass plate

The main purpose of this work is to develop a macro material constitutive model for inorganic glass response description under impact conditions. Firstly, the quasi-static and dynamic strength of soda-lime glass was obtained through uniaxial compression and combined compression-shear loading tests. The strain-rate and loading-path dependence of glass strength was observed from these experimental results. An improved model of impacted soda-lime glass plate was proposed based on the JH-2 model including the loading-path influence through an additional factor as a function of the Lode parameter. In commercial code Abaqus, the improved model is implemented through a user-defined material subroutine. Additionally, simulation of the static test, SHPB test, and impact test on glass specimens respectively is conducted to validate the model with updated material constants. The comparisons illustrate that the improved model of soda-lime glass provides better accuracy and efficiency predictions of glass responses at various loading conditions.

Plasticity-controlled failure of fibre-reinforced thermoplastics

Flow-induced fibre orientation generally causes anisotropy in the mechanical response of short fibre reinforced thermoplastics. In this manuscript, this anisotropy is studied for a wide selection of fibre-reinforced thermoplastics, focusing on the strain-rate dependence of the strength, and its relation to the stress-dependence of the lifespan under static load (creep rupture). It is demonstrated that, for short- as well as long-fibre reinforced thermoplastics, the influence of fibre-orientation and applied strain-rate on the tensile strength can be multiplicatively decomposed; the response is factorizable in load-angle and strain-rate. This factorizability appears to be generic to fibre-reinforced systems, since it is observed regardless of fibre type, fibre length, fibre weight fraction, matrix type and level of interfacial fibre–matrix interaction. The apparent factorisation of fibre-orientation and strain-rate dependence of the fracture stress opens up a possibility to considerably reduce experimental efforts required for composite characterisation. Subsequently, an anisotropic viscoplastic model previously developed by van Erp et al. (2009), is analysed for its capability describe the observed factorizability. This model is expressed in a form of an associated flow rule, which combines the Eyring flow equation, required to describe the strain rate dependence at a reference orientation, with the Hill equivalent stress formulation to capture the load-angle dependence. The model not only describes the load-angle and strain-rate dependence of the tensile strength accurately, but, in combination with a critical strain concept, it also provides accurate predictions of the creep lifetime for different loading angles.

Evaluation of impact ductile fracture behaviour of low carbon austenitic stainless steel SUS304L using damage mechanics model

To clarify the applicability of the Gurson-Tvergaard-Needleman (GTN) model for impact ductile fracture behaviour, SHB test was reproduced by finite element analysis (FEA). The strain-rate dependence of the strength for austenitic stainless steel JIS SUS304L was obtained by tensile tests at quasi-static strain rate and impact strain rate. The CowperSymonds power law, which takes into the strain-rate dependence of strength, and the GTN model implemented in the commercial FEA code were used to simulate for impact ductile-fracture behaviour. GTN model parameters were determined by minimizing the difference between the simulated and measured stress-strain curve using response surface method. SHB test was simulated using GTN model obtained from quasi-static tensile test result. Simulation results did not occur the necking and fracture on the specimen. The fracture surfaces were observed by SEM micrograph. The appearance of ductile fracture since dimples are observed, regardless of the strain rate. It is necessary to adjust the parameter to accelerate the nucleation of the void. By identifying the GTN parameters in consideration of the strain rate dependence including impact strain rate. It would be possible to improve the simulation accuracy of impact ductile fracture behaviour.

Mathematical modeling of progressive failure of two-layer metal-plastic shells of revolution under pulse loading

A technique for numerical analysis of nonlinear dynamic deformation and progressive failure of multi-layered metal-plastic shells of revolution is developed with account for their strain-rate dependent strength characteristics. The kinematic deformation model of a layered package is based on the non-classical theory of shells. The geometric dependencies are formulated based on the quadratic version of the nonlinear theory of elasticity. The relationship between stress and strain tensors in a composite macrolayer is established on the basis of Hooke’s law for an orthotropic body combined with the theory of effective modules, while for metal macrolayer, within the flow theory with linear hardening. The process of progressive layer-by-layer failure is described in the framework of the degradation model of stiffness characteristics. The strain rate dependence of stiffness and strength characteristics of composite materials is accounted for. An energetically consistent system of equations of motion for a shell of revolution is constructed using the principle of possible displacements. A numerical method for solving the problem is based on an explicit variational-difference scheme. The adequacy of the proposed technique was considered on the problem of unsteady deformation of a cylindrical shell subjected to pulse pressure simulating an explosion in the shell center.

Effect of the Mass Fraction of Ice on the Strain Rate Dependence of Strength under Dynamic Fracture of Frozen Soil

Experimental dependences of the strength of frozen sandy soil on strain rate are analyzed using a structural–temporal approach. Results of dynamic uniaxial compression tests at a temperature of −18°C and strain rates of 400 to 2600 s−1 of frozen sandy soil specimens of two types with an ice mass fraction of 10 and 18% measured at room temperature are presented. The strain rate dependence at different freezing temperatures of frozen sand with an ice mass fraction of 30% is studied using known experimental data.

Numerical Simulation of the Effect of Deformation Rates on the Dynamic Strength of GFRP Cylindrical Shells

A technique for the numerical analysis of nonlinear dynamic deformation and progressive failure of cylindrical glass-fiber plastic shells is developed with account of their strain-rate-dependent strength characteristics. The kinematic model of deformation of a layer package is based on a nonclassical theory of shells. The geometrical relations are constructed using the simplest quadratic variant of nonlinear elasticity theory. The relationship between the stress and strain tensors in a composite macrolayer is established on the basis of Hooke’s law for an orthotropic body, with account of volatility of the stiffness and strength characteristics of the multilayer package due to a local failure of some elementary layers of the composite and the strain-rate dependence of strength characteristics. An energy-consistent resolving system of dynamics equations for composite cylindrical shells is obtained as a result of minimization of the functional of total energy of the shell as a three-dimensional body. The numerical method for solving the initial boundary-value problem is based on an explicit variationaldifference scheme. The reliability of the technique developed was confirmed by a satisfactory agreement of calculation results with experimental data. For different shell reinforcement structures, qualitative differences in the character and size of failure zones were found, which were calculated by the model considering the strain-rate dependence of strength or their constancy.

Geotechnical laboratory testing and data interpretation for biosolids and sewage sludge

Biosolids and sewage sludge are difficult, challenging and unconventional geomaterials with some distinctive properties, including extremely high water content and plasticity; low particle density; high organic content; very high compressibility, creep and strain rate dependence of strength; a viscous gel-like pore fluid phase; extremely low permeability coefficient; and a propensity to degrade, producing copious amounts of biogas. The geotechnical properties and behaviour of these materials have been comprehensively reviewed in a companion paper previously published in this journal. The purpose of the present review paper is to describe necessary procedural modifications to standard geotechnical laboratory test methods, including associated analyses and data interpretation procedures, to obtain meaningful determinations of their index, compaction, compression, consolidation and permeability properties and their undrained and effective-stress strength parameter values. Specific aspects investigated include a modified curve-fitting technique for interpreting oedometer strain–time data, rapid and accurate means for undrained strength measurement and the significance and effects of ongoing biodegradation for long-term tests, as well as the corrosive nature of these materials. Many of the procedural modifications to geotechnical laboratory testing and nuances in the data interpretation presented in this paper should be transferable to the testing of other biodegradable soil and soil-like materials.

The mechanical response of commercially available bone simulants for quasi-static and dynamic loading

Bone is a complex hierarchal structured material with varying porosity and mechanical properties. In particular, human cranial bone is essentially a natural composite consisting of low porosity outer and inner tables and a cancellous interior, or diploë. Experimental studies of biomechanically accurate cranial bone analogues are of high importance for biomechanical, forensics, and clinical researchers, which could improve the understanding and prevention of traumatic injury. Many reported studies use commercially available bone surrogates to draw biomechanical and forensics conclusions; however, their mechanical properties are not tabulated over a range of strain rates. This study elucidates the mechanical viability of three leading commercially available bone surrogates, i.e. Synbone, Sawbone, and Bonesim, over a large range of strain rates (10−3 to 103 s−1). Quasi-static compression testing was conducted using a universal testing machine and a Split-Hopkinson Pressure bar system equipped with high-speed video was used to determine the dynamic mechanical behavior of these materials. Micro-computed X-ray tomography (XRT) were performed on each material to investigate their pore structures and distributions. All materials exhibited strain rate dependent strength behavior, particularly at high loading rates (≥103 s−1). The Young's modulus was found to increase with strain rate from 10−3 to 10−1 s−1 for transversely and longitudinally loaded surrogate materials except for Synbone and the higher density Bonesim. The higher density Bonesim was determined to be the most suitable cranial bone simulant tested based on a combination of transverse Young's Modulus (1500 MPa), yield strength (19 MPa), ultimate strength (49 MPa), and ultimate strain (17%). These materials show limited promise for applications where the measured elastic properties and strengths are of interest.

Geotechnical properties of compacted biosolids for monofill design, As-Samra, Jordan

This paper presents the results of a comprehensive geotechnical laboratory testing for the assessment and design of a proposed biosolid monofill facility at the As-Samra Waste Water Treatment Plant (WWTP) in Jordan. Previous landfill operations for biosolid materials typically involved co-disposal or lagooning of the dewatered biosolid slurry. However, it is proposed that the solar-dried As-Samra WWTP biosolid material will be placed in a new monofill facility at the site. This approach is suited to the As-Samra desert climate, since the material’s water content can be readily reduced to between 60 and 100% in evaporation lagoons. New insights were gained on the strength and compressibility of the non-inundated and saturated compacted biosolid materials, including their (a) very low normalised undrained strength ratio and effective angle of shearing resistance values for the saturated normally consolidated states of 0·14 and 15°, respectively; (b) very high strain rate dependency of strength; and (c) extremely low permeability coefficient values on the order of 10−12 m/s for compaction at approximately 100% water content. The paper concludes with recommendations on the appropriate water content range for compaction of the material in the proposed monofill and the selection of design strength values for geotechnical stability analysis.

A Simple Effective Stress Approach for Modeling Rate-Dependent Strength of Soft Clay

This paper proposes a simple effective stress method for modeling the strain rate-dependent strength behavior that is experienced by many fine-grained soils in offshore events when subjected to rapid, large strain, undrained shearing. The approach is based on correlating the size of the modified Cam-Clay yield locus with strain rate, i.e., yield locus enlarging or diminishing dependent on the strain rate. A viscometer-based method for evaluating the needed parameters for this approach is provided. The viscometer measurements showed that strain rate parameters are largely independent of water content and agree closely with data from a previous study. Numerical analysis of the annular simple shear situation induced by the viscometer shows remarkable agreement with the experimental data provided the remolding-induced strength degradation effect is accounted for. The proposed method allows offshore foundation installation processes such as dynamically installed offshore anchors, free-falling penetrometer, and submarine landslides to be more realistically analyzed through effective stress calculations.

A nanoscale study of the negative strain rate dependency of the strength of metallic glasses by molecular dynamics simulations.

Compressive strength and deformation characteristics of a metallic glassy alloy related to strain rate are studied by molecular dynamics simulations. The negative strain rate dependency of strength is presented, i.e., compressive strength decreases with the increase of strain rate, which is well in line with the experimental results. The negative strain rate dependency of strength is explained from two aspects at the atomic scale of free volume and potential energy. Compressive strength is related to the free volume formation in a shear band, which is different from that in a metallic glass matrix. In addition, the relation of potential energy and temperature is also investigated, which indicates that thermal softening also plays an important role in the negative strain rate dependency of strength. The thermal-mechanical coupling mechanisms causing the negative strain rate dependency of the strength of the metallic glassy alloy are clarified. It is significant to explore the intrinsic deformation characteristics of the metallic glassy alloy under a high rate loading.

Impact Tensile Properties of Notched Titanium Alloy Bolt for Fairing Separation of Launch Vehicle

The payload fairing in Japan is fixed by a lot of notched bolts. These notched bolts were fractured by axial impact tensile using the explosive devices to separate the fairing. In this case, the stress waves and the oscillations propagate, which may seriously damage the satellites. In this study, the impact deformation and the fracture behavior of notched titanium alloy bolt was investigated using a split Hopkinson pressure bar method. The notched bolt specimen was made of commercial Ti-6Al-4V alloy. The maximum load value was increased with increasing the displacement rate. It can be said that the strain rate dependence of strength for Ti-6Al-4V alloy appeared. From the observation of fracture surface using a scanning electron microscope, compared with the quasi-static test, it was clear that the irregularities of the fractured surface at the impact tensile test became rough. Therefore, it was found that the brittle fracture was mainly observed due to the increase in displacement rate, which may mean that the mode of fracture changes from the transgranular to the intergranular. It was surmised that this change of fracture mode was caused by the high strain rate due to stress concentration of the notched part.

Dynamic Compressive Behaviour of Closed-Cell Foam Materials Using Load-Measuring Apparatus with Opposite Load-Cells

It is necessary to evaluate the mechanical properties of foam materials at wide range of strain rates, since these materials have the strain rate dependence of strength. In this study, we evaluated the dynamic compressive behaviour of the closed-cell foam materials using the load-measuring apparatus with opposite load-cells, which is applying the drop-weight testing machine. In order to measure large deformation at dynamic strain rate range, universal rate range load-cell, which can reduce the influence of the reflected stress wave, was used. In addition, load equilibrium can evaluate using opposite load-cells which consist of movable (drop-weight) and stationary load-cells. In this study, the commercially available ALPORAS closed-cell aluminum foam was used. From the results of quasi-static tests, three deformation processes of elastic response, plateau deformation and densification were confirmed in stress-strain relation. Within the set of experiments, the closed-cell aluminum foam was locally deformed from cells with low strength and the stress variation occurred during plateau deformation, regardless of the strain rate. In addition, it was clarified that the stress equilibrium was not achieved at the dynamic strain rate. This is thought to be a phenomenon caused by local deformation of cell structure.

Strain rate dependence of tensile strength and ductility of nano and ultrafine grained coppers

An ultrafine grained Cu with a wide distribution of grain size and an average grain size of d= 110nm was prepared by electric brush-plating technique. Tensile properties, microstructure and deformation surface morphologies of this ultrafine grained Cu were compared with two results on an electric brush-plated nanocrystalline Cu (d= 59nm) and an electrodeposited ultrafine grained Cu (d= 200nm) previously prepared by our group. Based on these comparisons, the strain rate dependences of strength and ductility of these three materials and underlying mechanisms were studied. It was revealed that the pronounced strain rate sensitivity (larger m value) of these three materials is a result of the competition between the dislocation and grain boundary mediated deformations. The grain boundary mediated deformation plays a very important role in controlling the tensile ductility of these three materials, which affects the deformation accommodation by promoting different modes of strain localization and hence leads to the completely different strain rate dependences of tensile ductility (the elongations decrease, remains unchangeable and increase with increasing strain rate).

Experimental and theoretical studies on inter-fiber failure of unidirectional polymer-matrix composites under different strain rates

Polymer-matrix composites (PMCs) are widely used in many fields. However, the accurate characterization of their failure behavior is still a challenge. At present, the inter-fiber failure of unidirectional PMCs under compression is not well predicted, and the corresponding strain rate dependent failure theory remains less explored. This paper aims to study and characterize the inter-fiber failure behavior of unidirectional PMCs under different strain rates. Unidirectional glass/epoxy specimens with various off-axis angles were tested at three strain rates (quasi-static, 383 and 646s−1), and the measured strain rate dependent strength is modelled by an empirical formula. To evaluate the test results, a new failure theory that incorporates strain rate effects is proposed. The theory is developed based on three different failure modes, with each represented by a new and simple formula. Comparison shows that the predicted failure envelopes and fracture angles are in excellent agreement with the experimental results.