Strain Rate Dependency Of Material Research Articles

Experimental characterization of material strain-rate dependence based on full-field Data-Driven Identification

Mechanical characterization usually relies on standardized sample geometries where homogeneous state of strain and stress are prescribed. Hence, many tests are required to capture the material response over various loading conditions. Using complex geometry allows for exploring wider domain in a single test but would require to have access to local strains and stresses to feed models. In that context, digital image correlation and clustering technique can be used to formulate an inverse problem able to identify fields of stress tensors without a priori constitutive modelling. This study explores the performances of a rate-dependent formulation of such a data-driven stress identification method, for capturing using a single test, the monotonic high strain-rate dependent response of a mild steel alloy. After presenting the problem formulation and resolution framework, a digital twin of a high speed tensile test performed on a notched sample geometry is used to explore identification performances. It allows defining confidence intervals depending on multiple indicators (stress magnitude, multiaxiality) and evaluate the range of strain-rate levels simultaneously captured. The method is eventually applied to a real experiment instrumented with high spatial resolution ultra high speed camera. Stress tensor fields are identified, within a 10 % confidence over the major part of the sample, and its material rate-dependence is retrieved from 20 to 300 s−1 and found in very good agreement with literature. This is the first experimental application of the DDI in a high strain-rate context. The proposed framework may substantially widen the sample design space for mechanical characterization but also allow for probing local stresses during dynamic localization processes where in-situ quantitative data are still missing.

Experimental and Numerical Assessment of the Impact Test Performance Between Two UHSS Toe Cap Models

This paper presents an integrated approach for an ultimate high-performance safety toe cap with significant milestones in slim design and weight saving. The study of crashworthiness properties was performed through impact-crash test conditions exploring the potential of applicant solutions by the combination of an advanced high-strength steel and enhanced geometric stiffening models. The structural response for a significant thickness reduction was assessed and it provides an evolved discussion for improvements in energy absorption capacity. The present case study focuses on two geometric models from the S3 slim toe cap development by prototypes made of a martensitic 1200 steel alloy. The comparison of results is complemented using numerical simulation models with mathematical description of the dynamic plasticity behaviour by applying a constitutive Cowper-Symonds equation with fundamental parameters for material strain-rate dependence.

Experimental determination and numerical prediction of the dynamic forming limits of a press hardened steel

Material characteristics such as yield strength, failure strain, strain hardening and strain rate sensitivity parameter are affected by loading speed. Therefore, the strain rate dependency of materials for plasticity and failure behavior is taken into account in crash simulations. Moreover, a possibility for consideration of instability at multi-axial dynamic loadings in crash simulations is the use of dynamic forming limit curves (FLC). In this study, the dynamic FLC of the press hardened automotive steel Usibor 1500 (AlSi coated 22MnB5) is investigated. The experimental results are obtained from a unique high-speed Nakajima setup. Two models are used for the numerical prediction. One is the numerical algorithm CRACH as part of the modular material and failure model MF GenYld+CrachFEM 4.2. Furthermore, the extended modified maximum force criterion considering the strain rate effect is also used to predict the dynamic FLC. The comparison of the experimental and numerical results are presented and discussed.

Transient Impact Analysis of Elastic-plastic Beam with Strain-Rate Sensitivity

The impact response of an elastic-plastic beam is highly complicated in nonlinear transient dynamics especially when the material's plasticity is strain rate dependent. To reduce the efforts required for the computational analysis, an analytical-numerical model (hybrid model) is proposed for the analysis of the transient response of the beam to sphere impact. The model couples two sub-models, a combined discretization model and a refined contact model. Both the sub-models incorporate the material strain rate dependence. The combined discretization model discretizes the beam in length direction by a dynamic substructure technique and in thickness direction by a finite difference technique to capture the beam wave propagations along the length and the stress variations along the thickness. The refined contact model extends the BD model [1] to sphere-beam impacts by introducing a new representative contact strain rate and a new unloading law to avoided the force discontinuity at the inception of unloading. The hybrid model is validated by the laboratory test performed for low-velocity impacts and by the three-dimensional finite element (FE) analysis implemented for moderate-velocity and moderate high-velocity impacts. The validations show that the hybrid model is accurate, highly efficient and suitable for the parametric study, especially for the study of impact-induced wave effects. By using the hybrid model, tests and FE analyses, the influences of the material strain rate sensitivity are investigated by comparing to the results of elastic plastic impact simulations ignoring the effect of strain rate. It is found that the influence of the strain rate dependence on the contact force-indentation relation is significant even in the low-velocity impacts. The influences of the strain rate dependence on the contact duration and maximum contact force are small, even for the impact velocity up to 30 m/s. The influences of the strain rate dependence on other impact responses are small in the low-velocity impacts, and increase with increasing of the impact velocity. A parametric analysis is conducted to investigate the effects of the impact conditions on the contact duration and coefficient restitution. Their map structures are complicated, depending upon the mass ratio and the impact position. A jumping/falling phenomenon for the variations of the contact duration and coefficient of restitution is found, which are caused by the multiple impacts.

Development of estimation method of strain rate dependency of materials based on a high-velocity impingement test with a solid sphere

Development of estimation method of strain rate dependency of materials based on a high-velocity impingement test with a solid sphere

One-dimensional modeling of necking in rate-dependent materials

This paper presents an asymptotically rigorous one-dimensional analytical formulation capable of accurately capturing the stress and strain distributions that develop within the evolving neck of bars and sheets of rate-dependent materials stretched in tension. The work is an extension of an earlier study by the authors on necking instabilities in rate-independent materials. The one-dimensional model accounts for the gradients of the stress and strain that develop as the necking instability grows. Material strain-rate dependence has a significant influence on the strain that can be imposed on a bar or sheet before necking becomes pronounced. The formulation in this paper enables a quantitative assessment of the interplay in necking retardation due to rate-dependence and that due to the development of hydrostatic tension in the neck. The connection with a much simpler long-wavelength approximation which does not account for curvature induced hydrostatic tension in the neck is also emphasized and extended.

Bending characterisation of a molten unidirectional carbon fibre reinforced thermoplastic composite using a Dynamic Mechanical Analysis system

The quality of forming simulations based on Finite Element methods is mainly determined by the accuracy of the material properties. Out-of-plane bending is one of the deformation mechanisms that govern the appearance of wrinkles while forming composite reinforcements. This paper proposes a new test method using a Dynamic Mechanical Analysis (DMA) system for the characterisation of longitudinal out-of-plane bending properties of molten unidirectional thermoplastics. Investigations are presented for a unidirectional carbon fibre reinforced polyamide 6 composite. Several standard bending test fixtures are assessed quasistatically at three temperatures and three test speeds with specimens of different geometries. Additional tests are conducted at forming temperature with the selected test arrangement. The evaluation of different approaches for the calculation of the bending modulus shows the interlaminar shear to be negligible. Results highlight an important material strain rate dependency. The evolution of the bending modulus satisfies a linear fitting within the range of data.

鋭い圧子押込みにおける応答曲面法を用いたCowper-Symonds構成式定数の決定

Instrumented indentation is widely used to investigate the elastic and plastic properties of mechanical materials. During an indentation experiment, a rigid indenter penetrates normally into a homogeneous solid, where the indentation load and the displacement are continuously recorded during loading and unloading. It was known that the micro-indentation test was strongly affected by the strain rate in the materials with strain rate dependence of strength. In the second report, the new approach for the evaluation of the strain rate dependence of materials was developed using the loading curvature-displacement relation obtained from the sharp indentation. Therefore, we attempted to use the response surface method in order to determine the constants for Cowper-Symonds constitutive equation (dynamic constants). First, the relationship between the dynamic constants and the loading curvature was constructed by the response surface, and then those were determined using the inverse analysis. It was confirmed that the dynamic constants could be obtained by substituting the result of the micro-indentation for the unknown materials into the response surface up to the strain rate of 102 s-1. By using this method, it is possible to evaluate the strain rate dependence of materials in such a strain rate range.

OS1521-163 インデンテーションにおける代表ひずみ速度の導入

Indentation is commonly used to investigate the elastic and plastic properties of materials, which include strain rate dependence. In this study, in order to propose a new indentation concept, which involves the representative strain rate, a finite element method analysis based on the strain rate dependence of materials was used. In order to generate an index of strain rate within the indentation, a strain rate distribution averaging was performed. The strain rate distribution was averaged using the critical and representative strain boundary values of the indentation. It was determined that the relationship between the average strain rate and the loading curvature could be expressed using the dynamic constants of the Cowper-Symonds equation. This allowed for the development of a modified Kick's law that included the effect of strain rate in the indentation analysis. Furthermore, the average strain rate calculated using the representative strain could be defined as the representative strain rate for the indentation from the results of a parametric analysis. These results depended on the work-hardening coefficient and the indenter angle. Therefore, the representative strain rate, which revealed a new indentation parameter, was proposed

Transition of mechanisms underlying the rate effects and its significance

The strain rate dependency of materials’ failure has been widely observed in experiments and simulations, yet its microscopic mechanism is still elusive due to the complexity of failure processes. In this work, modified molecular dynamics simulations are carried out to investigate the strain rate effect over a wide strain rate range. The results demonstrate three typical failure modes induced by the competition of two timescales involved. The transition of mechanisms underlying these failure modes is discussed with a simplified model. The corresponding analysis indicates that the thermal activation model offers a good prediction for the variation of failure strain with respect to applied strain rate for failure mode I; the coupled evolution of atomic motions and potential landscapes governs the failure mode II; and the failure mode III is a result of the rapid separation between loading and deformation parts of the sample.

Numerical Evaluation of Dynamic Behavior of Axial Crushing Honeycomb Based on Adhesively-Bonded Model

The axial crushing behavior of metal honeycomb was studied with laying emphasis on the effects of adhesively-bonded joint and strain rate dependence on its characteristics as an energy absorber. To introduce the influences of the plastic deformation of adhesive layer and the fracture of adhesively-bonded joint, the embedded-process-zone (EPZ) model was used. First, the axial crushing behavior of metal honeycombs (A3003 aluminum alloy and SUS430 stainless steel) was studied with changing the strain rate by low-speed and drop-weight experiments, and then the numerical model of honeycomb, which included EPZ model and the initial imperfection, was investigated by the explicit FEM code LS-DYNA. The mean buckling load calculated with EPZ model becomes smaller than that calculated with the combined model and agrees well with the experimental result. The effect of the strain rate dependence of material on the structure was also studied by the numerical simulation as well as by the experiment. A3003 honeycomb shows no strain rate dependence on the load –displacement relation while SUS430 honeycomb shows significant increase in the mean buckling load.

Mechanical Properties of Saturated Concrete Depending on the Strain Rate

This study investigates the influence of condensed water in concrete on the fracture mechanism of a concrete structure. The focus of this study is water pressure in concrete pores under loading with a high strain rate. First, uniaxial compression tests of saturated cylinder specimens containing various types of micro pore structures were conducted with different strain rates. The saturated concretes, especially those of low water-cement ratios, increased compression strength with increasing strain rate. Second, bending tests of rectangular beam specimens with and without rebar were conducted with different strain rates. As the strain rate increased, plain concretes and reinforced concretes showed an increase in tensile strength. These results suggest that dynamic responses of concrete structures are influenced by the strain rate dependency of material that is correlated with water content and micro pore structure.

OS1722 ハニカム構造の軸圧潰に見られる材料のひずみ速度依存性

The axial crushing behavior of metal honeycombs was studied primarily by the experiments with laying emphasis on the effects of strain rate on those characteristics as energy absorbers. To evaluate the strain rate dependence of materials, A3003 aluminum alloy, SUS430 stainless steel and C1100 tough-pitch copper were used to fabricate honeycomb structures in laboratory. Then, the axial crushing tests under low-speed and free-fall impacting conditions were carried out. SUS430 and C1100 show certain strain rate dependence so that fabricated honeycomb structures also show strain rate sensitivity to some extent. However, the deformation of axial crushing honeycomb is not uniform but is localized at each stage of the progressive plastic buckling. The results show the effect of strain rate on an indicator of energy absorption ability such as mean buckling stress is less than that on the flow stress of foil material itself. The numerical simulations, which took the influences of the plastic deformation of adhesive layer and the fracture of adhesively-bonded joint into consideration, were also conducted by the FEM code LS-DYNA to confirm and understand the behavior.

Estimation of the initial peak load for circular tubes subjected to axial impact

This paper discusses the estimation of the initial peak load for circular tubes subjected to axial impact based on a finite element analysis. The peak load depends on the material properties, tube geometries and impact velocity. By changing some parameters systematically, effects of material properties and tube geometries on the peak load are explored. Also, the effect of the impact velocity on the peak load implies both the inertia effect and the material strain rate dependency. By observing the axial stress distribution and deformation behaviour in detail, and by calculating the strain rate near the vertex of a wrinkle when the peak load is observed, both effects on the peak load are clarified. Moreover, an approximate equation to evaluate the peak stress is proposed and in good agreement with the FEM results and other researcher's results under a relatively low impact velocity ( V 0 < 40 m / s ).

Interface Forces in Laterally Impacted Steel Tubes

In engineering mechanisms, solid bodies frequently come to a contact with a variety of geometric and kinematic situations. There has been a trend to express the interaction of the contacted bodies in the form of equivalent interface forces. The interface force represents the level of load transferred from one body to another. In a static or quasi-static contact problem, the interface forces could be sensibly evaluated by integrating the normal and the shear stresses over the common interfaces. In a dynamic contact, the interface stresses and subsequently the interface forces happen to be more complicated. They are, furthermore, affected by other parameters such as inertia forces, stress waves propagation, the material strain rate dependency and damping. This paper reports interface forces recorded in a series of experimental impact tests on axially pre-compressed steel tubes along with those from the numerical simulations of the tests. To monitor the so called impact loads, two small steel rings as load cells have been built in the striker. Based on the experimental and numerical results, the concept of equivalent interface forces in the impacted tubes has been verified. It has been highlighted that the interface forces (or the impact loads) may vary on the striker or the specimen themselves, depending on the measuring locations. Effects of axial compressions on the interface forces picked up by the striker load cells, impact loads imparted to the specimen supports and on the impact duration have been discussed. It has been reported that the initial compression applied to the tubes does not remain constant during and after the impact event. The amount of variations also depends on the initial level of the tube compression.

Computational evaluation of strain-rate-dependent deformation behavior of rubber and carbon-black-filled rubber under monotonic and cyclic straining

The molecular chain network model for elastic deformation behavior and the reptation theory for viscoelastic deformation behavior are used to derive a constitutive equation for rubber. The new eight-chain-like model contains eight standard models consisting of Langevin springs and dashpot to account for the interaction of chains with their surroundings. Monotonic and cyclic deformation behavior of rubber with relaxation under different strain rates have been examined. The results reveal the roles of the individual springs and dashpot, and the strain rate dependence of materials in the monotonic and cyclic deformation behaviors, particularly softening and hysteresis loss, that is, the Mullins effect, occurring in stress–stretch curves under cyclic deformation processes. The validity of the results is checked through comparison with experimental results. The deformation behaviors of a plane strain rubber unit cell containing carbon-black (CB) under monotonic and cyclic straining are investigated by computational simulation using the proposed constitutive equation and homogenization method. The results reveal the substantial enhancement of the resistance of CB-filled rubber to macroscopic deformation, which is caused by the marked orientation hardening due to the highly localized deformation of rubber. The role of strain rate sensitivity on such characteristic deformation behaviors as increases in the resistance to deformation, hysteresis loss, and the effects of the distribution morphology and the volume fraction of CB on the deformation behavior is clarified. The increases in the volume fraction and in the aggregation of the distribution of CB substantially raise the resistance to deformation and hysteresis loss.

Strain Rate Dependent Micro- to Macroscopic Deformation Behavior of Carbon-Black Filled Rubber under Monotonic and Cyclic Straining

A constitutive equation of rubber is derived by employing a nonaffine molecular chain network model for an elastic deformation behavior and the reptation theory for a viscoelastic deformation behavior. The results reveal the roles of the individual springs and dashpot, and the strain rate dependence of materials in the monotonic and cyclic deformation behaviors, particularly softening and hysteresis loss, that is, the Mullins effect, occurring in stress-stretch curves under cyclic deformation processes of carbon black filled rubber..

Strain-Rate-Dependent Deformation Behavior of Carbon-Black-Filled Rubber under Monotonic and Cyclic Straining

The constitutive equation of rubber is derived by employing a nonaffine molecular chain network model for an elastic deformation behavior and the reptation theory for a viscoelastic deformation behavior. The results reveal the roles of the individual springs and dashpot, and the strain rate dependence of materials and disentanglement of molecular chains in the monotonic and cyclic deformation behaviors, particularly softening and hysteresis loss, that is, the Mullins effect, occurring in stress-stretch curves under cyclic deformation processes.

Coupled Plastic Wave Propagation and Column Buckling

The plastic buckling of columns is explored in a regime where plastic wave propagation and lateral buckling are nonlinearly coupled. Underlying the work is the motivation to understand and quantify the dynamic crushing resistance of truss cores of all-metal sandwich plates where each truss member is a clamped column. Members are typically fairly stocky such that they buckle plastically and their load carrying capacity decreases gradually as they buckle, even at slow loading rates. In the range of elevated loading rates of interest here, the columns are significantly stabilized by lateral inertia, resisting lateral motion and delaying buckling and loss of load carrying capacity to relatively large overall plastic strains. The time scale associated with dynamic axial behavior, wherein deformation spreads along the column as a plastic wave, is comparable to the time scale associated with lateral buckling such that the two phenomena are coupled. Several relevant problems are analyzed using a combination of analytical and numerical procedures. Material strain-rate dependence is also taken into account. Detailed finite element analyses are performed for axially loaded columns with initial imperfections, as well as for inclined columns in a truss core of a sandwich plate, with the aim of determining the resistance of the column to deformation as dependent on the loading rate and the relevant material and geometric parameters. In the range of loading rates of interest, dynamic effects result in substantial increases in the reaction forces exerted by core members on the faces of the sandwich plate with significant elevation in energy absorption.

Modeling and simulation of intersonic crack growth

Intersonic crack growth has been studied using an interfacial fracture model in which an additional material phase within a bonding layer is proposed to describe the failure behavior of the interface. In this material phase, a strain gradient based damage model is applied with a built-in cohesive law, which is governed by an material intrinsic length scale that bridges the mechanisms that operate at continuum mechanics scale and at smaller scales. Simulations of the intersonic crack growth experiments ( Rosakis et al., 1999; Rosakis, 2002) have been performed with varying material length scales and other parameters. The study is focused on two subjects: (1) the process of decohesion-induced cracking, explaining fracture process zone initiation and propagation as well as the corresponding contact mechanisms; (2) propagation speed, investigating the effects of length scales and loading parameters. The simulations reveal that a fracture process zone initiates first and extends with a speed faster than shear wave speed. After initiation, the crack speed exhibits oscillations with an average value between c s 2 and c l, where c s and c l refer to shear wave and dilatation wave speeds, respectively. In such a quasi-steady-state propagation, the crack opening profiles exhibit a time-invariant profile, while the fracture process zone size and decohesion energy remain constant. Contact between the crack faces is taken into account in the numerical simulations. A contact zone behind the crack tip has been captured which represents a self-healing-like mechanism. The leading edge of both the fracture process zone and the contact zone may cause strong shocks. When the average crack propagation speed approaches the supersonic region, two stress shocks radiate from the crack tip, corresponding to shear and dilatation wave radiation, respectively. The simulation results demonstrate that length and time scales play vital roles during crack propagation. Here the length scales refer to the bonding layer thickness and the material’s intrinsic length that governs energy dissipation during failure; whereas the time scales refer to the effects of material strain rate dependence, material failure speed, and wave propagation properties. A parameter R s, expressed as the ratio of material shear strength and the applied stress that is calculated from the remote imposed displacement boundary condition, is proposed to scale crack speed. Intersonic propagation occurs when R s is greater than a threshold value. The numerical computations are compared with experiments ( Rosakis et al., 1999; Rosakis, 2002) and the theoretical solution [Philos. Mag., A, in press], which demonstrates the trend that crack propagation is unstable in the open speed interval between c s and κ v c s ( 2 ⩽κ v <c l /c s ) whereas it is stable when the speed lies in the close interval between κ v c s and c l. The coefficient κ v is a function of material length scale, strain rate sensitivity, and boundary conditions. The moving particle finite element method, a newly developed meshfree method, and the pinball contact algorithm are applied in the numerical analysis.