Multiple Strain Rates Research Articles

Constitutive Models for Compressive Deformation of AZ80 Magnesium Alloy under Multiple Loading Directions and Strain Rates

Two constitutive models, the modified Johnson-Cook model and the logarithm linear relation model based on empirical approach and data analysis, were presented to illustrate compressive deformation of magnesium alloys AZ80 under multiple loading directions and strain rates. The results of stress-strain curve analysis and sensitivity index analysis suggested that the stress held large fluctuations in loading direction of 90°. Model testing signified that the logarithm linear relation model was more proper than the modified Johnson-Cook model in view of relative mean square error and correlation coefficients. Moreover, numerical simulation building on established models also indicated that the logarithm linear model is more precise than the modified Johnson-Cook model.

A constitutive model for ballistic gelatin at surgical strain rates

This paper describes a constitutive model for ballistic gelatin at the low strain rates experienced, for example, by soft tissues during surgery. While this material is most commonly associated with high speed projectile penetration and impact investigations, it has also been used extensively as a soft tissue simulant in validation studies for surgical technologies (e.g. surgical simulation and guidance systems), for which loading speeds and the corresponding mechanical response of the material are quite different. We conducted mechanical compression experiments on gelatin specimens at strain rates spanning two orders of magnitude (~0.001–0.1s−1) and observed a nonlinear load–displacement history and strong strain rate-dependence. A compact and efficient visco-hyperelastic constitutive model was then formulated and found to fit the experimental data well. An Ogden type strain energy density function was employed for the elastic component. A single Prony exponential term was found to be adequate to capture the observed rate-dependence of the response over multiple strain rates. The model lends itself to immediate use within many commercial finite element packages.

Effect of Pre-Stress on the Dynamic Tensile Behavior of the TMJ Disc

Previous dynamic analyses of the temporomandibular joint (TMJ) disc have not included a true preload, i.e., a step stress or strain beyond the initial tare load. However, due to the highly nonlinear stress-strain response of the TMJ disc, we hypothesized that the dynamic mechanical properties would greatly depend on the preload, which could then, in part, account for the large variation in the tensile stiffnesses reported for the TMJ disc in the literature. This study is the first to report the dynamic mechanical properties as a function of prestress. As hypothesized, the storage modulus (E′) of the disc varied by a factor of 25 in the mediolateral direction and a factor of 200 in the anteroposterior direction, depending on the prestress. Multiple constant strain rate sweeps were extracted and superimposed via strain-rate frequency superposition (SRFS), which demonstrated that the strain rate amplitude and strain rate were both important factors in determining the TMJ disc material properties, which is an effect not typically seen with synthetic materials. The presented analysis demonstrated, for the first time, the applicability of viscoelastic models, previously applied to synthetic polymer materials, to a complex hierarchical biomaterial such as the TMJ disc, providing a uniquely comprehensive way to capture the viscoelastic response of biological materials. Finally, we emphasize that the use of a preload, preferably which falls within the linear region of the stress-strain curve, is critical to provide reproducible results for tensile analysis of musculoskeletal tissues. Therefore, we recommend that future dynamic mechanical analyses of the TMJ disc be performed at a controlled prestress corresponding to a strain range of 5–10%.

Strain Rate and Loading Waveform Effects on an Energy-Based Fatigue Life Prediction for AL6061-T6

The energy-based lifing method is based on the theory that the cumulative energy in all hysteresis loops of a specimens' lifetime is equal to the energy in a monotonic tension test. Based on this theory, fatigue life can be calculated by dividing monotonic strain energy by a hysteresis energy model, which is a function of stress amplitude. Recent studies have focused on developing this method for a sine wave loading pattern—a variable strain rate. In order to remove the effects of a variable strain rate throughout the fatigue cycle, a constant strain rate triangle wave loading pattern was tested. The testing was conducted at various frequencies to evaluate the effects of multiple constant strain rates. Hysteresis loops created with sine wave loading and triangle loading were compared. The effects of variable and constant strain rate loading patterns on hysteresis loops throughout a specimens' fatigue life are examined.

Behaviour of Brittle Material in Multiple Loading Rates Under Uniaxial Compression

It is of great importance to investigate the effect of loading rate on the behaviour of brittle material such as concrete and rock because engineering structures are subjected to multiple loading conditions. Although material behaviour under single loading mode has been extensively studied, very limited research has been conducted to investigate the performance of brittle materials subjected to varying loading conditions. This paper presents an experimental study of the effects of single and multiple strain rates (e) on cement mortar samples. The first set of samples was loaded at constant strain rates until failure. For the remaining samples, the first strain rate (0.005 mm/s) was applied to the sample up to a predetermined load, and then the second strain was initiated immediately by using the specially-designed gear system in place in the compression rig. As expected, the increase in strain rate showed an increase in peak strength of the sample with reduced ultimate strain. For multiple strain modes, it was observed that the highest peak strength occurred when the second strain was applied at 50 % of the peak strength of the first strain.

Dynamic modeling for rate-dependent and mode-dependent cohesive interface failure analysis

Accurate modeling of interface failure represents an important consideration for analysis cases such as adhesive bonds or phase interface failure of inhomogeneous materials. In the current work, a cohesive element based model for interface failure has been developed in the context of a butterfly-type Hopkinson Bar interface specimen. Simulation has enabled insight into the dynamic in-situ stress state and crack growth under impact for property determination and test specimen evaluation. A failure criterion has been successfully employed and agrees closely with experimental results at multiple strain rates. Strain rate effects and fracture mode effects are implemented to modify the allowable strain to failure at the interface. Calculated fracture toughness values and crack propagation rates have compared closely to published experimental results at multiple strain rates. An analytical parametric evaluation of the interface failure model has been performed to illustrate the relative importance of material properties and failure behavior.

Identifying a Minimal Rheological Configuration: A Tool for Effective and Efficient Constitutive Modeling of Soft Tissues

We describe a modeling methodology intended as a preliminary step in the identification of appropriate constitutive frameworks for the time-dependent response of biological tissues. The modeling approach comprises a customizable rheological network of viscous and elastic elements governed by user-defined 1D constitutive relationships. The model parameters are identified by iterative nonlinear optimization, minimizing the error between experimental and model-predicted structural (load-displacement) tissue response under a specific mode of deformation. We demonstrate the use of this methodology by determining the minimal rheological arrangement, constitutive relationships, and model parameters for the structural response of various soft tissues, including ex vivo perfused porcine liver in indentation, ex vivo porcine brain cortical tissue in indentation, and ex vivo human cervical tissue in unconfined compression. Our results indicate that the identified rheological configurations provide good agreement with experimental data, including multiple constant strain rate load/unload tests and stress relaxation tests. Our experience suggests that the described modeling framework is an efficient tool for exploring a wide array of constitutive relationships and rheological arrangements, which can subsequently serve as a basis for 3D constitutive model development and finite-element implementations. The proposed approach can also be employed as a self-contained tool to obtain simplified 1D phenomenological models of the structural response of biological tissue to single-axis manipulations for applications in haptic technologies.

A mechanistic study for strain rate sensitivity of rabbit patellar tendon

The ultrastructural mechanism for strain rate sensitivity of collagenous tissue has not been well studied at the collagen fibril level. Our objective is to reveal the mechanistic contribution of tendon’s key structural component to strain rate sensitivity. We have investigated the structure of the collagen fibril undergoing tension at different strain rates. Tendon fascicles were pulled and fixed within the linear region (12% local tissue strain) at multiple strain rates. Although samples were pulled to the same percent elongation, the fibrils were noticed to elongate differently, increasing with strain rate. For the 0.1, 10, and 70%/s strain rates, there were 1.84±3.6%, 5.5±1.9%, and 7.03±2.2% elongations (mean±S.D.), respectively. We concluded that the collagen fibrils underwent significantly greater recruitment (fibril strain relative to global tissue strain) at higher strain rates. A better understanding of tendon mechanisms at lower hierarchical levels would help establish a basis for future development of constitutive models and assist in tissue replacement design.

Comparisons of percolation segregation of multi-size and continuous mixtures at multiple strains and strain rates

Percolation segregation of fines in multi-size and multi-component mixtures was quantified and compared with continuous mixtures. In addition to size; shape and density also affect the number of multi-size components needed to predict the percolation of fines for continuous mixtures. Processing condition such as strain rate also played the role in determining number of components needed to predict the percolation of fines in continuous mixture.

Response of turbulent boundary layers to multiple strain rates

Many practical applications, such as in blade cascades and turbomachinery, involve inhomogeneous turbulent shear flows subjected simultaneously to multiple strains. In principle, the applied strain can be combined to yield an effective strain. However, no simple stress–strain relation is capable of establishing turbulent stress or energy balance in the mean or on an instantaneous basis. In the current investigation, a turbulent boundary layer is examined in the presence of convex curvatures of different strengths combined with streamwise (favourable and adverse) pressure gradients, with various values of pressure gradient ratio, (∂P/∂s)/(∂P/∂n). Measurements of the mean and turbulent parameters and flux Richardson number show appreciable changes, mainly in the outer portion of the boundary layer (y+ > 100). The turbulent burst frequency, particularly at the location of application of the additional strain rate, also changes relative to its value with wall curvature alone.Three primary observations from these experiments are as follows: (i) in all cases, the mean velocity profile and all of the measured Reynolds stresses collapse in the near-wall region using standard inner scaling; (ii) the applied strains combine nonlinearly, with one of the strains dominating the local flow during its development; (iii) the ratio of the radial to axial pressure gradient magnitude influences both classical turbulence correlations and mean flow, as well as the physical production cycle of turbulence; and (iv) application rate of newly introduced strain rates is at least as important as their magnitudes.

Turbulent Boundary Layers Subjected to Multiple Strains

Turbomachinery flows can be extremely difficult to predict, due to a multitude of effects, including interacting strain rates, compressibility, and rotation. The primary objective of this investigation was to study the influence of multiple strain rates (favorable streamwise pressure gradient combined with radial pressure gradient due to convex curvature) on the structure of the turbulent boundary layer. The emphasis was on the initial region of curvature, which is relevant to the leading edge of a stator vane, for example. In order to gain better insight into the dynamics of complex turbulent boundary layers, detailed velocity measurements were made in a low-speed water tunnel using a two-component laser Doppler velocimeter. The mean and fluctuating velocity profiles showed that the influence of the strong favorable pressure augmented the stabilizing effects of convex curvature. The trends exhibited by the primary Reynolds shear stress followed those of the mean turbulent bursting frequency, i.e., a decrease in the bursting frequency coincided with a reduction of the peak Reynolds shear stress. It was found that the effects of these two strain rates were not superposable, or additive in any simple manner. Thus, the dynamics of the large energy-containing eddies and their interaction with the turbulence production mechanisms must be considered for modeling turbulent flows with multiple strain rates.

Fundamental characterisation of hemisphere free bulging using superplastic 8090 Al–Li sheets

Hemisphere free bulging of a superplastic 8090 Al–Li sheet was carried out, with particular emphasis given to the superplastic behaviour over the low strain regime ɛ=0−0·7. Various pressurising cycles, including constant pressure, constant strain rate, and multiple strain rate bulging, were performed to characterise the superplastic behaviour in terms of strain rate variation, thickness distribution, and evaluation of the strain rate sensitivity (m) of the sheet during biaxial bulging. For constant strain rate bulging, a modified Ghosh and Hamilton (GH) model and a model developed by the present authors (HL) have been used to simulate the necessary pressure profiles. Two different constitutive equations, extracted from uniaxial tensile tests, were used in the study. The modified GH model applied σ=Kεm as the constitutive equation, i.e. considering only the m value in the simulation, while the H L model incorporated the strain hardening exponent (n) additionally into the constitutive equation for the simulation: i.e. the equation σ=εɛnεm was used. The HL model can also be applied to simulate the multiple stage strain rate forming route. Based on the analyses, the material superplasticity characteristics obtained from uniaxial tensile tests were seen to be reliably applicable to equibiaxial sheet bulging. The equibiaxial straining condition was not obeyed exactly except at the pole. With the consideration of initial work hardening contribution towards the constitutive equation, the simulated results seemed to agree better with the experimental data. With further straining, the rate sensitivity increased and work hardening decreased, thereby a multiple strain rate bulging path, including a high initial rate followed by several lower strain rates, would be able to fully utilise the higher values of m and n during each straining stage. The thickness uniformity as well as the total forming time could thus be improved and shortened.MST/3107