Strain Rate Dependence Research Articles

Visco-hyperelastic material model fitting to experimental stress–strain curves using a genetic algorithm and its application to soft tissue simulants

Ballistic impacts on human thorax without penetration can produce severe injuries or even death of the carrier. Soft tissue finite element models must capture the non-linear elasticity and strain-rate dependence to accurately estimate the dynamic human mechanical response. The objective of this work is the calibration of a visco-hyperelastic model for soft tissue simulants. Material model parameters have been calculated by fitting experimental stress–strain relations obtained from the literature using genetic algorithms. Several parametric analyses have been carried out during the definition of the optimization algorithm. In this way, we were able to study different optimization strategies to improve the convergence and accuracy of the final result. Finally, the genetic algorithm has been applied to calibrate two different soft tissue simulants: ballistic gelatin and styrene–ethylene–butylene–styrene. The algorithm is able to calculate the constants for visco-hyperelastic constitutive equations with high accuracy. Regarding synthetic stress–strain curves, a short computational time has been shown when using the semi-free strategy, leading to high precision results in stress–strain curves. The algorithm developed in this work, whose code is included as supplementary material for the reader use, can be applied to calibrate visco-hyperelastic parameters from stress–strain relations under different strain rates. The semi-free relaxation time strategy has shown to obtain more accurate results and shorter convergence times than the other strategies studied. It has been also shown that the understanding of the constitutive models and the complexity of the stress–strain objective curves is crucial for the accuracy of the method.

Strain rate dependence of mechanical behavior in an AlSi10Mg alloy with different states fabricated by laser powder bed fusion

The strain rate dependence of mechanical behavior in an AlSi10Mg alloy with different states fabricated by laser powder bed fusion (LPBF) was investigated systematically via thermodynamic calculations, microstructure characterization and mechanical characteristic evaluation in the present study. The results show that there is a close relationship among the material state, microstructure and dynamic mechanical behavior. Before tensile deformation, the as-built specimen possesses a fine equiaxed grain structure and a typical cellular structure surrounded by continuously distributed particles; the annealed specimen has coarser equiaxed grain structures and particles, but no cellular structure is present. Both the as-built and annealed specimens exhibit weak strain rate sensitivity, and the strain rate sensitivity parameters are 0.01 and 0.024, respectively. Under specific strain rate conditions, the as-built specimen has a higher strength and lower elongation than the annealed specimen. After tensile deformation, there is a significant increase in the dislocation density. Independent of the material state, the dislocation density increases with increasing strain rate. Compared with the as-built specimen, the annealed specimen has a stronger strain rate sensitivity because of the greater dislocation density variation.

Surface micro-morphology model involved in grinding of GaN crystals driven by strain-rate and abrasive coupling effects

The complexity of the interaction between the workpiece and abrasives, the characterisation difficulty of the strain-rate effect, and the analytical difficulty of brittle-ductile coexistence removal pose significant challenges in surface micro-morphology modelling of brittle-solid grinding. To overcome these bottlenecks, a theoretical model of the normal scratching force driven by the strain-rate effect was developed to verify the strain-rate sensitivity coefficients of gallium nitride (GaN) crystals. Impact scratching tests with a single grit further emphasised that the brittle-to-ductile transition and subsurface damage behaviour of GaN crystals exhibited a distinct strain-rate dependence. Subsequently, a theoretical model of the surface micro-morphology involved in the grinding of GaN crystals was developed by comprehensively considering the strain rate, abrasive coupling effect, time evolution, abrasive randomness, and elastic-to-plastic and brittle-to-ductile transition depths. The simulated results of the model agreed well with the experimental results, with an average error of <10 %. The model indicated that the ground surface micro-morphology and roughness were insensitive to variations in the grinding depth. Under the allowable conditions of the grinder stiffness and dynamic balance, appropriately increasing the wheel speed and grinding depth, decreasing the feed speed, and refining the abrasive size could effectively improve the proportion of ductile removal during the grinding of brittle solids. The results not only enhance the understanding of the abrasive coupling effect on surface micro-morphological evolution, material removal, and damage accumulation, but also provide theoretical guidance for the parameter optimisation involved in the grinding of brittle solids.

Evolution of Displacement Speed Statistics During Head-On Flame-Wall Interaction within Turbulent Boundary Layers

ABSTRACT The statistical behaviours of the density-weighted displacement speed and its curvature and strain rate dependence during head-on interaction of statistically planar premixed flames have been analysed based on Direct Numerical Simulations. The analysis has been conducted within turbulent boundary layers featuring inert walls, under both isothermal and adiabatic wall boundary conditions. The flame quenches due to heat loss when it reaches close to the wall in the case of isothermal wall boundary condition. By contrast, the flame can propagate all the way to the wall before extinguishing due to the consumption of reactants in the case of adiabatic wall boundary conditions. Thus, the effects of thermal expansion, quantified by dilatation rate, and flame normal acceleration during flame-wall interaction in the case of the isothermal wall are weaker than that in the case of the adiabatic wall case due to flame quenching. This gives rise to significant differences in the curvature and strain rate dependences of the reactive scalar gradient magnitude, which affects the statistical behaviours of the reaction and normal diffusion components of density-weighted displacement speed including their mean values, widths of their probability density functions, and their local strain rate and curvature dependences. It has been found that the interaction of near-wall vortical structures with flame surface increases the range of curvature variation during head-on interaction, which acts to widen the probability density function of the density-weighted displacement speed. This trend is relatively stronger for the isothermal wall boundary condition because of the larger variation of the reaction rate component of the density-weighted displacement speed due to local flame quenching, which also acts to widen the range of the density-weighted displacement speed variation in comparison to that in the case of adiabatic wall boundary conditions. Although the qualitative nature of curvature, strain rate, and stretch rate dependences of the density-weighted displacement speed remain unaffected by the wall boundary condition, the strength of the correlation changes with the progress of head-on interaction. It has been found that the negative correlation between the density-weighted displacement speed and flame curvature weakens with the progress of head-on interaction, which gives rise to a reduction in the strength of the correlation between the density-weighted displacement speed and flame stretch rate. Similarly, the correlation between the tangential strain rate and the density-weighted displacement speed weakens with the progress of head-on interaction. Detailed physical explanations are provided for these behaviours, and their modeling implications are indicated.

Research on Viscoelastic Impact Damage Constitutive Model and Its Behavioral Characteristics

To investigate the damage characteristics of viscoelastic materials under various impact scenarios, this study presents a viscoelastic impact damage constitutive model that incorporates a material coefficient, a variable fractional-order differential operator, and a damage factor. Split Hopkinson Pressure Bar experiments are conducted under single-impact and repeated-impact conditions. The results indicate that nonlinear features in stress-strain curves at different stages, exhibiting prominent strain rate dependency near the stress peak point in the single-impact scenario. In the repeated-impact scenario, the stress peak points decrease as the impact times increase, resulting in a corresponding decline in the material's load-bearing capacity. Furthermore, strain rate escalates the strain rate increases with an increase in impact times, making the material more susceptible to deformation. Parameter fitting and Sobol sensitivity analysis utilizing experimental data from both scenarios have been employed to explore the effects and patterns of single-parameter and multi-parameter coupling on the model, accurately delineating their influence. The findings reveal a strong coupling relationship among various parameters of the viscoelastic impact damage constitutive model in multiple impact scenarios, showing higher sensitivity to fluctuations in the viscoelastic coefficient and damage factor. These analyses have demonstrated the accuracy of the viscoelastic impact damage constitutive model in capturing dynamic impact damage characteristics of viscoelastic materials across various scenarios.

Dynamic strengthening of UHMWPE yarns by incorporating ZrO2/PU coatings

Wrapping is an effective technique for reducing defects in fabric weaving and promoting even wetting in composite manufacturing, which is potential to enhance the impact resistance of armor materials. In this study, we impregnated UHMWPE yarns with a polyurethane (PU) compound and cured them to create composite yarns, and ZrO2 was introduced to improve the toughness. The microstructures were analyzed using three-dimensional X-ray computed tomography, optical microscopy, and scanning electron microscopy (SEM). Quasi-static and dynamic tensile experiments were conducted using a universal testing machine and Kolsky tension bar, respectively. High-speed imaging was used to capture the real-time failure process, and post-fracture analysis was performed to examine the fracture morphology. The effects of strain rate, gauge length, and the presence of PU and ZrO2 on the mechanical behavior of the yarns were investigated. The results showed that the peak force of the composite yarns with PU coatings exhibited strain-rate dependency at low strain rates (below 4.4 × 10−2 s−1) but became insensitive to strain rate in the higher range of 4.4 × 10−2 s−1 to 1500 s−1. Furthermore, the introduction of ZrO2 effectively increased the peak force, potentially by strengthening the bonding between individual fibers within the yarn.

Silicone‐containing polyurea elastomer possessing main‐chain boron–oxygen bonds with delayed stress relaxation and improved adhesive properties

AbstractPolyurea (PU) elastomers have attracted considerable attention in the field of protective polymeric coatings. In this work, a dithiol‐terminated boronic ester was synthesized and used to incorporate dynamic boron–oxygen (B–O) bonds in the PU main chain based on thiol isocyanate while amino‐terminated polydimethylsiloxane (PDMS) was introduced to retain good chain flexibility. The modified PU elastomer was found to have a microphase‐separated structure in which the hard blocks served as physical crosslinks. The glass transition temperature (Tg) slightly increases when dynamic B–O bonds exist while further introduction of PDMS soft segment can lower Tg to −55.63 °C. The introduction of dynamic B–O bonds and diminished hydrogen bonding led to a decrease in mechanical strength and elongation at break. Interestingly, the simultaneous incorporation of PDMS and dynamic B–O bonds is favorable for strain rate dependence and suppressing stress relaxation. The potential for bond‐exchange interactions between the dynamic B–O bonds and hydroxyl groups on metal surfaces substantially improved the adhesion of the PU elastomer to metal substrates. Therefore, our work can offer valuable insights for the structural design of functional PU coatings tailored for anti‐impact applications. © 2024 Society of Chemical Industry.

A constitutive model for rate-dependency analysis of open hole woven composites under compression loading

The mechanical performance of composite materials under impact phenomena is of interest for several industries. Although the effect of the strain rate on composites significantly affects the behaviour of these materials, most studies describe the mechanical behaviour of CFRP laminates neglecting the strain rate dependence. This work presents a new constitutive model to numerically implement the change of in-plane properties of an plain weave CFRP (AGP193) over a wide range of strain rates (up to 500 s−1). Open hole compression tests are used to validate the model under quasi-static and dynamic loading. The importance of implementing the influence of strain rate on mechanical properties is illustrated by the maximum strength plot and the stress–strain history, both of which would be underestimated without the inclusion of strain rate in the model. The strain rates at the edge of the hole greatly exceed the average values in the sample, leading to an underestimation of the apparent strength up to 100% if the strain rate effect is not taken into account.

Dynamic deformation behavior of single phase VNbTa medium-entropy alloys

In this study, the deformation behavior of body-centered-cubic (BCC) VNbTa medium-entropy alloy (MEA) was studied under different strain rates ranging from 10−3 s−1 to 5000 s−1 using screw-driven testing machine and split Hopkinson pressure bar (SHPB), respectively. The alloy presents an outstanding synergy of strength and plasticity without any adiabatic shear bands even at a strain rate of 5000 s−1. Moreover, the yield strength of the alloy displays an obvious strain rate dependence, increasing by ∼94.4% from 842 MPa at 10−3 s−1 to 1637 MPa at 5000 s−1. The strain rate sensitivity (SRS) factor m and highest temperature rise under dynamic loading is calculated to be 0.2991 and 182 K, respectively, which means a strong strain rate hardening and thermal softening resistance. Microstructure evolution analyses demonstrate a transition of deformation mechanism from single dislocation slip controlling in low strain rate to a synergy of mechanical twinning and dislocation slip in high strain rate. Therefore, the excellent dynamic mechanical properties could be attributed to the synergistic effects of the strong strain rate hardening and thermal softening resistance, the mechanical twins, and the cell structures and microbands derived from dislocation slip controlling. In addition, the dynamic deformation behavior of VNbTa could also be described by a classical Johnson-Cook model. Combining the excellent cryogenic temperature mechanical properties (tensile strength of ∼1930 MPa and fracture elongation ∼27%), the present work further indicates that the VNbTa MEA has great potential for engineering applications under some extreme circumstances.

Thermo-Mechanical Behavior and Strain Rate Sensitivity of 3D-Printed Polylactic Acid (PLA) below Glass Transition Temperature (Tg).

This study investigated the thermomechanical behavior of 4D-printed polylactic acid (PLA), focusing on its response to varying temperatures and strain rates in a wide range below the glass transition temperature (Tg). The material was characterized using tension, compression, and dynamic mechanical thermal analysis (DMTA), confirming PLA's strong dependency on strain rate and temperature. The glass transition temperature of 4D-printed PLA was determined to be 65 °C using a thermal analysis (DMTA). The elastic modulus changed from 1045.7 MPa in the glassy phase to 1.2 MPa in the rubber phase, showing the great shape memory potential of 4D-printed PLA. The filament tension tests revealed that the material's yield stress strongly depended on the strain rate at room temperature, with values ranging from 56 MPa to 43 MPA as the strain rate decreased. Using a commercial FDM Ultimaker printer, cylindrical compression samples were 3D-printed and then characterized under thermo-mechanical conditions. Thermo-mechanical compression tests were conducted at strain rates ranging from 0.0001 s-1 to 0.1 s-1 and at temperatures below the glass transition temperature (Tg) at 25, 37, and 50 °C. The conducted experimental tests showed that the material had distinct yield stress, strain softening, and strain hardening at very large deformations. Clear strain rate dependence was observed, particularly at quasi-static rates, with the temperature and strain rate significantly influencing PLA's mechanical properties, including yield stress. Yield stress values varied from 110 MPa at room temperature with a strain rate of 0.1 s-1 to 42 MPa at 50 °C with a strain rate of 0.0001 s-1. This study also included thermo-mechanical adiabatic tests, which revealed that higher strain rates of 0.01 s-1 and 0.1 s-1 led to self-heating due to non-dissipated generated heat. This internal heating caused additional softening at higher strain rates and lower stress values. Thermal imaging revealed temperature increases of 15 °C and 18 °C for strain rates of 0.01 s-1 and 0.1 s-1, respectively.

The transition from strain rate insensitivity to sensitivity of Ti–6Al–4V alloys deformed at cryogenic temperature

The aim of the present study is to elucidate the strain rate (ε˙) dependency of Ti–6Al–4V alloys under cryogenic deformation conditions, inspired by our recent observations of strain rate insensitivity in pure titanium as well as the temperature effect on the stacking fault energy. Unlike the pronounced strain rate sensitivity at ambient temperatures, a strain rate insensitivity when ε˙ < 10−2 s−1 and strain rate sensitivity when ε˙ > 10−2 s−1 were observed during cryogenic deformation. Subsequent analyses underscored the pivotal role of stacking faults in modulating the transition from strain rate insensitivity to sensitivity with increasing strain rates. The present study therefore enriches the existing knowledge on the mechanism of cryogenic deformation, offering guidance for the engineering of high-performance titanium alloys.

Compressive mechanical properties of styrene-butadiene rubber under medium-low strain rates: Experiments and modeling

Styrene-butadiene rubber (SBR) is widely employed as a cushioning material in engineering applications to resist impact loadings due to its excellent mechanical properties and energy absorption capacity. This paper aims to investigate the compressive mechanical properties and constitutive model of SBR under medium–low strain rates both experimentally and theoretically. Firstly, quasi-static and dynamic compression tests of SBR were carried out under the strain rate up to 220 s−1 using an electronic universal testing machine and a drop-weight machine, respectively. Subsequently, the effect of loading rate on mechanical properties, strain rate sensitivity and energy absorption capacity was examined. The results indicate that SBR exhibits visco-hyperelastic characteristics with reversible compression deformation and strain rate dependency, ie., the yield stress, flow stress and dynamic increase factor (DIF) increase approximately exponentially with increasing logarithmic strain rate. In addition, the SBR exhibits excellent energy absorption capacity during compression, especially under higher strain rates and larger strain levels. Finally, a visco-hyperelastic constitutive model was proposed by replacing the nonlinear spring with a hyperelastic element in Zhu-Wang-Tang (ZWT) viscoelastic constitutive model to describe the nonlinear mechanical behaviors in SBR, and an acceptable agreement between experimental results and model predictions were observed. The findings of this research can provide a valuable guide for designing and optimizing the impact resistance of SBR structures.

Effect of the loading-rate and stress state on the constitutive modelling and fracture of 2205 Duplex stainless steel

Shear cutting is a high-speed forming process where material separation is involved. The nature of the process leads to high strain rates and temperatures on the sheared zone of the material subjected to the operation. In this work, the mechanical behavior in terms of flow stress, plastic deformation and fracture of a 2205 Duplex stainless steel sheet is determined. Uniaxial tension, uniaxial compression, stack compression, plane strain tension and simple shear tests at different angles with respect to the rolling direction of the metal sheet are performed to determine the anisotropic behavior of the material. Strain rate and temperature dependence of the flow stress and the plastic behavior of the material is determined through notched tensile tests performed under various temperatures (20°C, 100°C, 300°C and 500°C) and strain rates (0.001 s-1, 10 s-1 and >100 s-1). Finally, fracture behavior under various stress states is determined through notched tensile, central hole, in-plane shear and plane strain tests. The temperature and strain rate dependence of the fracture behavior is determined through notched tensile, in-plane shear and plane strain tests performed under various temperatures (20°C, 100°C, 300°C and 500°C) and strain rates (0.001 s-1, 10 s-1 and >100 s-1). The anisotropic behavior and work hardening of the material are modelled by the Hill48 yield function and Swift-Hockett-Sherby hardening law, respectively. Among the two ductile fracture models tested, Hosford-Coulomb model showed the best agreement and is therefore used to account for the temperature and strain rate effects on the fracture behavior. By combining these three models, an accurate reproduction of the mechanical behavior of the 2205 Duplex stainless steel sheet is achieved.

Characterisation of Polyurethane-urea as Leading-Edge Erosion Resistant Materials of Wind Turbine Blades

Surrounded by oceans, building offshore wind turbines is a great strategy for archipelago countries, like Indonesia, to harvest renewable energy from wind. However, because of high rainfall rate, water droplet erosion on wind turbine blades is inevitably to be one of the most challenging problems. It causes decreasing produced energy and increasing cost of maintenance and repairment. A novel coating material which has better mechanical properties is therefore required. As a preliminary step, this work aims to characterise thermal and mechanical properties of soft and hard polyurethane-urea (PUU). In this work, the materials are soft PUU30 which has a hardness of 30 shore A, and hard PUU95 which has a hardness of 95 shore A. Thermal properties are characterised by Differential Scanning Calorimetry (DSC), while mechanical properties are investigated by tensile test at various strain rates. The results show that PUU95 has a higher strain rate dependence on modulus, tensile strength, and strain at break, which need to be considered for application regarding the range of wind speeds.

Dynamic tensile behavior and constitutive model of a novel high-strength and high-toughness plate steel

The dynamic tensile behavior of a novel-developed plate steel with high strength and toughness is investigated. Uniaxial tensile tests are conducted at various strain rates varying from 0.1 s−1 to 1000 s−1, and then scanning electron microscope and electron backscattered diffraction analyses are performed on tensile specimens at failure. A large and homogeneous deformation is demonstrated during the tension and small necking is observed at failure; all test results reveal the strain rate dependency of this novel plate steel: with an increase in strain rate, the yield strength, ultimate tensile strength, and total elongation increase, whereas the uniform elongation decreases. Microstructure analyses find dimple fracture surface and considerable deformation twins and dislocations, confirming the high strength and high ductility of the novel plate steel. The density of twins and dislocations demonstrates a positive correlation with the increasing strain rate, aligning with the variations observed in the mechanical properties. Engineering stress–strain curves exhibit a necking lag effect at high strain rates, and this effect is considered when solving the true stress–strain relationships by a developed hybrid experimental–numerical method. A modified Johnson-Cook model considering the power law strain rate effect and thermal softening effect caused by adiabatic temperature rise is finally proposed and verified. This work explores the dynamic mechanical behavior of the novel plate steel at different strain rates, promoting its application in aseismic design and impact resistance engineering.

Numerical and analytical studies of multi-cell steel-concrete-steel sandwich panels under blast load

The steel-concrete-steel (SCS) sandwich panel possesses exceptional resistance and good integrity, making it successfully applied in protective engineering. Aiming at improving the blast resistance of the structure, a novel multi-cell steel-concrete-steel (MCSCS) sandwich panel was proposed as an alternative to the traditional SCS panel. In this paper, the finite element (FE) model of the MCSCS panel under blast load was first constructed, and the modeling method was verified to be reasonable against field blast tests. Then, an analytical model for predicting the blast response of the MCSCS panel was established based on the equivalent single-degree-of-freedom (SDOF) system, and the strain rate effect was incorporated into the analytical model via employing the material models with strain rate dependence. Finally, three damage criteria for the MCSCS panel under blast load were proposed, and Pressure-Impulse (P-I) diagrams corresponding to different damage levels were constructed via the validated analytical model. Additionally, based on the established analytical model, the accuracy of simplifying the blast pressure history into the triangle form was verified. Numerical and analytical results indicate that the blast resistance of the MCSCS panel is significantly enhanced with the increase of the steel faceplate thickness, and the MCSCS panel exhibits superior blast resistance with the load acting on the top plate rather than bottom plate. In addition, owing to the arrangement of the L-shaped and side stiffeners, the MCSCS panel possesses preferable integrity, and its blast resistance is nearly unaffected by the spacing of headed stud.

Effects of the strain rate in compression of electrodeposited gold micro-pillars toward the design of MEMS components

In this study, the strain rate dependence in yield strengths of electrodeposited gold micro-pillars is evaluated for the design of movable components in MEMS devices. The micro-pillars are fabricated from electrodeposited gold by focused ion beam system. The strain rate dependence is quantified by the strain rate sensitivity, and the strain rate sensitivity is calculated from the yield strength obtained from compression tests of the gold micro-pillars having different sizes at different strain rates. An increase in the yield strength following a reduction in the pillar size is observed, which is the sample size effect. Also, weakening of the yield strength is observed following a decrease in the strain rate, which is the strain rate dependence, and the strain rate sensitivity of the gold micro-pillars is found be at roughly 0.03.

Strain Rate Dependence of Amorphous Phase Instability in Semicrystalline Polymers: Insights from the Scale of Lamellar Stacks

Strain Rate Dependence of Amorphous Phase Instability in Semicrystalline Polymers: Insights from the Scale of Lamellar Stacks

Effect of padeye offset ratio on keying behaviours and capacity of square plate anchors in clay

This paper reports the effect of padeye offset ratio on the keying behaviours and capacity of square plate anchors in clay. The investigation is conducted through three-dimensional large deformation finite element analyses using the Remeshing and Interpolation Technique with Small Strain in ABAQUS. Strain rate dependency of the undrained shear strength and soil remoulding are accounted for adopting an extended Tresca model. The results from LDFE analyses are compared with existing analytical solutions, centrifuge test data, and numerical results; with reasonable agreement obtained. Parametric analyses are then carried out varying several critical factors including initial embedment depth, load eccentricity, padeye offset ratio, soil sensitivity, and soil strength heterogeneity. It is seen that the padeye offset has significant influence on the ultimate loss of embedment and capacity under vertical loading. To assess the keying behaviour of square plate anchors in clay, an equivalent soil strength incorporating strain rate dependency and remoulding is adopted. A combined factor defined as a function of the initial embedment depth and equivalent soil strength is used to estimate the ultimate loss of embedment. An equivalent ultimate bearing capacity factor is shown to be a function of the initial embedment depth, padeye offset ratio, and load eccentricity.

Strain Rate Dependence of Strain-Induced Martensitic Formation and Tensile Ductility in SUS304 Stainless Steel

Strain Rate Dependence of Strain-Induced Martensitic Formation and Tensile Ductility in SUS304 Stainless Steel