Strain Rate Dependence Research Articles

Mixed-mode dynamic fracture behavior of a rubber toughened epoxy adhesive under stress wave loading

This work seeks to measure mixed-mode fracture parameters for a dynamically growing crack in a core shell rubber toughened epoxy adhesive (EPONTM 828 with PARALOID™ EXL-2691J particles). Digital image correlation technique coupled with ultrahigh-speed photography and a hybrid finite element-based post-processing approach are used to extract fracture parameters. The dynamic loading is accomplished by using a striker to induce stress waves in an incident bar in contact with a free-standing semi-circular specimen. A companion finite element analysis is performed for investigating suitable experimental parameters and configurations for implementing the approach and determining specific experimental parameters (crack length, crack angle, and impact velocity) necessary to achieve the desired experimental conditions (mode mixity at crack initiation and strain rate). The critical fracture parameters are used to generate mixed mode fracture envelope and fracture toughness-mode mixity relationship for the material. Further investigation is carried out to evaluate various fracture criteria for predicting initial crack kink angles. The measured dynamic fracture quantities are also compared with the quasi-static counterparts to assess strain rate-dependence of the adhesive. The results reveal a decrease in critical stress intensity factors of approximately 10 % and 30 % for the mode I and mode II states, respectively, with increasing strain rate. Post-initiation, the dynamic crack propagates at a near-constant mode I stress intensity factor of ∼1.4 MPa-√m. Under dynamic conditions, the critical, effective stress intensity factors are relatively constant with respect to mode mixity. This is in contrast to quasi-static results where the effective values increased with respect to mode mixity. Experimentally measured crack kink angles agree well with those predicted by the maximum energy release rate criteria and the maximum tangential stress criteria, particularly under mode I dominant conditions.

Effects of water droplet injection on turbulent premixed flame propagation: a direct numerical simulation investigation

The influence of water droplet injection on the propagation rate of statistically planar stoichiometric n-heptane-air flames has been analysed based on three-dimensional carrier phase Direct Numerical Simulations for different turbulence intensities and different initially mono-sized droplets. It has been found that most water droplets do not completely evaporate within the flame due to their large latent heat of evaporation for the conditions considered here. Thus, the cooling effect due to the extraction of latent heat during the evaporation of water droplets dominates over the dilution of the concentration of reactants and gives rise to smaller reaction rate of reaction progress variable and thicker flame front than in the corresponding premixed turbulent flame without droplets. These effects (a) strengthen with decreasing droplet size due to higher rate of evaporation for smaller droplets, but (b) weaken with an increase in turbulence intensity. The interaction of water droplets with the flame affects the density-weighted displacement speed through its reaction and molecular diffusion components and the magnitudes of these components remain much greater than the components due to cross-scalar dissipation rate and two-phase coupling. The flame-water droplet interaction for the parameter range considered here acts to reduce the mean density-weighted displacement speed, consumption speed and turbulent flame speed, and this reduction becomes increasingly prominent with decreasing droplet diameter. However, it has been found that the presence of water droplets does not alter the qualitative nature of the strain rate and curvature dependences of both density-weighted displacement speed and consumption speed for the range of parameters considered here, but the correlation strength is altered by the presence of water droplets.

Dynamic compressive response of porcine muscle measured using a split Hopkinson bar system with a pair of PVDF force transducers

The classic metallic Split Hopkinson Pressure Bar (SHPB) cannot capture the transmitted signal accurately when measuring soft biological tissue, because of the very low wave impedance and strength of this material. So the dynamic compressive response of porcine muscle has been investigated by using a modified SHPB. The forces on both ends of the sample measured using Polyvinylidene fluor (PVDF) transducers were applied to calculate the stress in the specimen instead of the strain gauge signal on the transmitted bar. Moreover, a circular cardboard disk pulse shaper was applied for generating a suitable incident pulse to achieve stress equilibrium and constant strain rates in the specimens. Then, the dynamic mechanical properties of porcine muscle parallel and perpendicular to the fiber directions were measured, and the stress equilibrium process during loading was analyzed, as well as the inertia-induced extra stress being corrected. Furthermore, quasi-static tests were conducted at two different strain rates to investigate the strain rate dependence using a universal material testing machine. The results show that the stress-strain curves are sensitive to strain rate in the two different loading directions. The compressive stress perpendicular to the fiber direction is stiffer than that parallel to the fiber direction. In addition, a strain rate-dependent constitutive model was developed based on the mechanical response of the muscle at different strain rates and fitted to the experimental data. The results show that the overall fit is good, and the constitutive model could describe the muscle's dynamic mechanical properties.

A visco-elastoplastic constitutive model of aircraft polymethylmethacrylate related to strain rate and temperature

The visco-elastoplastic mechanical behavior related to the applied strain rate and temperature around the glass transition temperature of Polymethylmethacrylate (PMMA) has been systematically investigated. The uniaxial tensile test was performed at strain rate and temperature rangs 1.0 × 10−4–1.0 × 10−2 s−1 and 363–393 K, respectively, and the Dynamic Mechanical Analysis (DMA) test was carried out between 363 K and 413 K at various frequencies. Moreover, the robust complex constitutive model considering the temperature and strain rate effect is proposed. A nonlinear viscoelastic model is established to describe the viscoelastic response on the basis of the Zhu-Wang-Tang (ZWT) model and the time temperature equivalence principle, including the dependence of strain rate and temperature. Considering the yield stress, the cooperative model is adopted. The viscoplastic mechanical response is manifested as the competition performance of the softening deformation and hardening behavior. The predicted mechanical responses maintain good consistency with the experimental results, indicating that the visco-elastoplastic constitutive model proposed can accurately predict the mechanical behavior of PMMA materials within the imposed strain rate and near the glass transition temperature range.

Influence of water on deformation and failure of gypsum rock

While water is known to significantly reduce the strength of rocks, there remains a paucity of data on water-weakening of gypsum. Here, we quantify water-weakening in a natural gypsum facies from Monferrato (Italy) by performing experiments on nominally dry, oil-saturated, and water-saturated samples. Uniaxial and conventional triaxial experiments revealed significant water-weakening in Monferrato gypsum as well as a strong strain-rate dependence of uniaxial compressive strength. Moreover, uniaxial creep tests showed significant time-dependent deformation in samples saturated with sulphate over-saturated water, but not in dry and oil-saturated samples. The creep phenomenology is similar to that observed in other rock types and is consistent with stress-corrosion microcracking, which is supported by our microstructural observations. However, we systematically recorded more inelastic strain in samples deformed at low strain-rates suggesting that additional mechanisms were also active. Comparing our new data on short-term strength with published results for other rock types, we conclude that, when saturated with water in equilibrium with the rock, weakening in gypsum is not notably higher than in other rocks and is partially due to a reduction of fracture toughness in the presence of water.

Nano-mechanical properties of Mo coating prepared on Invar alloy substrate by double glow plasma surface alloying

In this work, surface Mo alloying was realized on Invar alloy using double glow plasma surface alloying technology. The microstructure and phase constitution of Mo-modified coating were determined by using X-ray diffraction and scanning electron microscopy. The surface modification effect and loading strain rate (LSR) dependency of Mo coating were presented qualitatively and quantitatively via nanoindentation method based on continuous stiffness measurement technique. Results showed that the received Mo coating with a thickness of approximately 10 μm was compact and homogeneous. The phase constitution consisted of pure Mo phase. Double glow plasma surface molybdenizing improved the surface hardness and elastic modulus remarkably. Indentation response showed obvious LSR dependency. Under different LSRs, hardness and plasticity exponent increased with LSR, while elastic modulus and contact stiffness basically remained stable. Meanwhile, creep displacement and creep strain rate sensitivity exponent were positively correlated with LSR.

Analysis of low velocity impact properties of basalt fiber composites considering strain rate effect

This study focuses on the strain rate effect on the mechanical properties and damage evolution of basalt fiber reinforced composites subjected to low-velocity impact. A constitutive model is developed to accurately analyze the failure behavior of BFRP laminates. The strain-rate-dependent (SRD) model puts emphasis on a modified stress-strain relationship described by dynamic increase factor (DIF) to update mechanical properties timely during the impact loading and the damage evolution simulation is performed with the finite element code of ABAQUS software. The results shown in the LVI simulation confirmed the validity of the SRD model in comparison with the conclusions of experiments. Furthermore, detailed comparisons are discussed between the strain rate dependent (SRD) model and the strain rate independent (SRI) model under various simulations of different impact energy, thickness, and ply angles of laminates.

Experimental investigations of the human oesophagus: anisotropic properties of the embalmed mucosa–submucosa layer under large deformation

Mechanical characterisation of the layer-specific, viscoelastic properties of the human oesophagus is crucial in furthering the development of devices emerging in the field, such as robotic endoscopic biopsy devices, as well as in enhancing the realism, and therefore effectiveness, of surgical simulations. In this study, the viscoelastic and stress-softening behaviour of the passive human oesophagus was investigated through ex vivo cyclic mechanical tests. Due to restrictions placed on the laboratory as a result of COVID-19, only oesophagi from cadavers fixed in formalin were allowed for testing. Three oesophagi in total were separated into their two main layers and the mucosa–submucosa layer was investigated. A series of uniaxial tensile tests were conducted in the form of increasing stretch level cyclic tests at two different strain rates: 1% s^{-1} and 10% s^{-1}. Rectangular samples in both the longitudinal and circumferential directions were tested to observe any anisotropy. Histological analysis was also performed through a variety of staining methods. Overall, the longitudinal direction was found to be much stiffer than the circumferential direction. Stress-softening was observed in both directions, as well as permanent set and hysteresis. Strain rate-dependent behaviour was also apparent in the two directions, with an increase in strain rate resulting in an increase in stiffness. This strain rate dependency was more pronounced in the longitudinal direction than the circumferential direction. Finally, the results were discussed in regard to the histological content of the layer, and the behaviour was modelled and validated using a visco-hyperelastic matrix-fibre model.

Strain rate dependence of tensile properties and strengthening mechanism of Ti6Al4V alloy undergoing different coverage layers of laser shock peening

Understanding the response of the Ti6Al4V alloy undergoing different coverage layers of laser shock peening (LSP) and the strain rate dependence of tensile properties is indispensable for its wide applications. Herein, the Ti6Al4V alloy specimens subjected to different coverage layers of LSP were employed in the uniaxial tensile testing with the strain rate of 0.001 s−1, 0.005 s−1, 0.01 s−1, and 0.02 s−1. The effects of the coverage layer on the tensile properties and its sensitivity to the strain rate were determined. The relationship between the microstructural morphologies, tensile behaviors, and strengthening mechanism were revealed. Moreover, the corresponding fracture behaviors of the tested specimens were summarized. It evidently shows that, the tensile properties and fracture behaviors of the Ti6Al4V alloy subjected to LSP treatment strongly depend on the strain rate. The ultimate tensile strength and the total elongation exhibit reverse trends with increasing strain rates and coverage layers, also, the typical ductile fracture pattern gradually evolves into the mixed ductility/cleavage fracture simultaneously. Upon the increasing plastic deformation process of LSP, the dislocation density, as well as the grain size are two intrinsic factors for controlling the strain hardening behavior and strain rate sensitivity, and the deformation twin provides another alternative factor.

Strain-Rate Dependence of Tensile Behavior in Commercial-Grade Tungsten-Effect of Recrystallization Condition.

The tensile deformation behavior of double-forged (DF-W) and recrystallized (RX-W) commercial-grade tungsten was investigated at 700 °C. With increasing strain rate, the dominant dynamic recrystallization (DRX) mechanism changes from continuous dynamic recrystallization (CDRX) to discontinuous dynamic recrystallization (DDRX). For DF-W, pre-existing sub-grains promote CDRX and associated a high-DRX fraction, resulting in reduced post-necking strain under a static condition. With increasing strain rate, a shift in the restoration mechanism from CDRX to DDRX contributes to the enhanced ductility in DF-W, while RX-W shows enhanced flow hardening without a loss of ductility. These results suggest that the strain-rate dependence of mechanical behavior depends on the initial microstructure.

An isogeometric finite element formulation for boundary and shell viscoelasticity based on a multiplicative surface deformation split

AbstractThis work presents a numerical formulation to model isotropic viscoelastic material behavior for membranes and thin shells. The surface and the shell theory are formulated within a curvilinear coordinate system, which allows the representation of general surfaces and deformations. The kinematics follow from Kirchhoff–Love theory and the discretization makes use of isogeometric shape functions. A multiplicative split of the surface deformation gradient is employed, such that an intermediate surface configuration is introduced. The surface metric and curvature of this intermediate configuration follow from the solution of nonlinear evolution laws—ordinary differential equations—that stem from a generalized viscoelastic solid model. The evolution laws are integrated numerically with the implicit Euler scheme and linearized within the Newton–Raphson scheme of the nonlinear finite element framework. The implementation of membrane and bending viscosity is verified with the help of analytical solutions and shows ideal convergence behavior. The chosen numerical examples capture large deformations and typical viscoelasticity behavior, such as creep, relaxation, and strain rate dependence. It is also shown that the proposed formulation can be straightforwardly applied to model boundary viscoelasticity of 3D bodies.

Unravelling the Size‐Dependent Mechanical Properties of Nanocrystalline Face‐Centered‐Cubic Metals: From the Dislocation Point of View

The grain size dependence of strain rate sensitivity, apparent activation volume, and yield stress of nanocrystalline (NC) face‐centered‐cubic metals (FCC) are modeled based on the bow‐out model of single dislocation. It is found that the grain size limitation on the dislocation length gives rise to the grain size effects on the mechanical properties. The model gives predictions that when temperature is at or below room temperature and the strain rate is in the quasistatic range, dislocation‐mediated mechanisms play a dominant role in the plastic deformations of FCC NC metals even for the grain size of several nanometers, which is consistent with known experimental and simulation results. Based on the model, abnormal mechanical phenomena of nanostructured metals, such as the appearance of the inverse Hall–Petch relationship, the existence of the critical grain size, and its strain rate dependence, are well predicted and interpreted.

Development of estimation method for material property under high strain rate condition utilizing experiment and analysis

Safety countermeasures have been implemented in nuclear power plants in Japan under the new nuclear regulation. The importance of structural integrity of components which are attacked by tornado missile has been growing as one of the countermeasures. In the case of impact analysis for tornado missile, strain rate dependency needs to be considered in the stress strain relationship, which is different from static analysis. However, it is difficult to obtain the data of stress strain relationship which strain rate is over 103 s−1 due to the restriction of test equipment. Therefore, a new method to estimate strain rate dependency of stress strain relationship on the high strain rate condition was developed. An inverse analysis using the deformation data obtained by the Taylor impact test and FEM analysis was applied in the method. Stress strain relationship estimated by the method was verified by comparing it to Split Hopkinson Bar (SHB) test result. It was confirmed that the method could estimate strain rate dependency of stress strain relationship accurately.

Identification Method for Material Constants in Johnson–Cook Model Associated With Strain-Rate and Temperature Sensitivities Using Ball Impact and Indentation Tests

Abstract The Johnson–Cook (JC) flow stress model can simply express the strain-rate and temperature dependencies of the flow stress. We previously proposed a concept of a simple identification method for material constants in the JC model associated with the strain-rate and temperature sensitivities (JC parameters C and m) at high-strain rates. However, several issues still exist in our method for practical use. In this study, we modified our method to identify both the JC parameters C and m. The fundamental concept was formulated based on the requirement that the normalized indentation depths obtained from the ball impact and instrumented ball indentation tests are equal to each other. In addition, the conversion factor was derived to transfer from the impact velocity to the strain rate. The ball indentation and impact analyses based on a finite element method were conducted to verify the established method. The analysis results obtained under idealized conditions demonstrated that C and m can be accurately identified using the established method, even at exceeding 104 s−1. Changes in the radius of the impactor are more effective in obtaining different strain rates than changes in the impact velocity because the identification accuracy can be ensured at lower than 200 m/s.

Multi-Scale Modelling of Plastic Deformation, Damage and Relaxation in Epoxy Resins.

Epoxy resin plasticity and damage was studied from molecular dynamic simulations and interpreted by the help of constitutive modelling. For the latter, we suggested a physically motivated approach that aims at interpolating two well-defined limiting cases; namely, pulling at the vanishing strain rate and very rapid deformation; here, taken as 50% of the speed of sound of the material. In turn, to consider 0.1–10-m/s-scale deformation rates, we employed a simple relaxation model featuring exponential stress decay with a relaxation time of 1.5 ns. As benchmarks, deformation and strain reversal runs were performed by molecular dynamic simulations using two different strain rates. Our analyses show the importance of molecular rearrangements within the epoxy network loops for rationalizing the strain-rate dependence of plasticity and residual stress upon strain reversal. To this end, our constitutive model reasonably reproduced experimental data of elastic and visco-elastic epoxy deformation, along with the maximum stress experienced before fracturing. Moreover, we show the importance of introducing damage elements for mimicking the mechanical behavior of epoxy resins.

Strain Rate Dependences of Dynamic Fracture Toughness and Fracture Energy of Rocks

Strain Rate Dependences of Dynamic Fracture Toughness and Fracture Energy of Rocks

In Situ Measurement of Instantaneous Viscosity Curve of Fluids in a Reserve Tank

A novel method enabling in situ measurement in a reserve tank for evaluating an instantaneous viscosity curve is presented. This aims to satisfy the practical demand of industrial production process for monitoring real-time rheological properties without taking samples. With applicable ranges of shear rate and viscosity, O(10–1–102 s–1) and O(10–2–100 Pa·s), it enables evaluation of fluid properties having shear strain rate dependence, based on ultrasonic spinning rheometry. Since this method evaluates the characteristic of shear thinning viscosity while changing the fluid temperature in a reserve tank, some useful examples are expected as further applications for measuring viscosity during chemical reaction processes, such as gelation, hydrolysis, and polymerization. Efficacy of the method evaluating rheological properties is validated by numerical and experimental results.

Strain rate dependence of the effect of intergranular carbides on the resistance to stress corrosion cracking initiation of alloy 690 in simulated PWR primary water

The stress corrosion cracking (SCC) initiation of alloy 690 in simulated PWR primary water was evaluated in constant extension rate tensile tests with different strain rates. The SCC initiation was inhibited by intergranular carbide precipitation. However, the carbide effect weakened with increasing strain rate. The SCC mitigation effect of carbides mainly arises from the carbides’ ability to impede the transfer of dislocations across grain boundaries and delay the local break-down of surface oxide films. However, dislocations accumulated near the grain boundary can promote intergranular oxidation which induces cracking after the oxide film fails.

Phase transition in medium entropy alloy CoCrNi under quasi-isentropic compression

Under high strain-rate loading, prominent increases in pressure usually triggers phase transition (PT), but the concomitant temperature rise may also cause melting. Quasi-isentropic (QI) compression provides a strategy to explore solid-state phase transition by reducing the temperature rise while retaining high pressure. Using large-scale molecular dynamics simulations, we investigate PTs in single crystal CoCrNi medium entropy alloys (MEAs) under QI compression. With the applied strain rates ranging from 108 s−1 to 1011 s−1, the strain-rate dependence and anisotropy of yield stress and solid-state PT path are revealed by comparing the mechanical responses along three compressed crystallographic orientations ([100], [11¯0], and [111]). Positive strain-rate sensitiveness is found in the yield stress along the [11¯0] and [111] directions, while insensitiveness along the [100] direction. Various PTs occur alongside massive plastic deformation in the post-yield regime. As the strain rate rises, face-centered-cubic (FCC) to body-centered-cubic (BCC) PT overrides the stacking fault-induced hexagonal-close-packed (HCP) phase formation and dominates the plasticity for the [100] loading. By contrast, crystalline PTs give way to amorphization for [11¯0] and [111] loading at high strain rates. Chemical short-range order hinders dislocation slip and promotes dislocation interactions, which further facilitate early formation of the BCC phase, suggesting a potential strategy to tailor polymorphism in MEAs.

Strength evaluation of CFRP structure of high pressure hydrogen tank based on mesoscale analysis

For designing with rigorous cost reduction and safety, high pressure hydrogen tanks manufactured from carbon fiber reinforced plastic (CFRP) of fuel cell vehicles, a method that can precisely predict the burst pressures of the tank is urgently needed. CFRP layers of tanks are formed with complicated mesostructured consisting of carbon fiber bundles and matrix resin using a filament winding process. A methodology that approaches by using cross shaped specimens to present fiber bundle conditions in CFRP layer of the tank is scrutinized. From the analysis and experiment with the specimen, it was found that strain rate dependency and tensile compression asymmetry of the resin have a great influence in addition to the fiber strength in the fiber direction on the CFRP fracture process. Burst pressures were predicted by CFRP mesoscale model with the load and boundary condition from macroscale analysis of conventional axisymmetric continuum model of the tank and validated through an actual tank burst test. As the results, we found the burst pressure of tank could be accurately predicted based on carbon fiber ruptures in the mesoscale model.