Strain Rate Dependent Material Model Research Articles

Calibration of tensile tests in drop-weight impact machine and implementation in simulation of Charpy impact tests

Material modeling and simulation of deformation under very high loading rate in the dynamic/impact range are applied in crash resistance, ballistic impact analysis, and other time-sensitive phenomena. Servo-hydraulic UTM tensile test data from medium to higher strain rate > (500 s-1) is reliable but expensive and complexity in experiment. Tensile testing at very high strain rate (upto 1500 s-1) can be done in a drop-weight impact testing machine with a special fixture and the impactor velocity controls strain rate. In INSTRON CEAST 9350 drop weight impact testing machine tensile tests are conducted at four velocities for amour steel. A 5MHz data acquisition system (DAQ) measures strain in specimen gauge length mounted with high-elongation strain gauge. An extensometer is used to calibrate the strain gauge in a quasi-static 10-4 s-1 tensile test. Tensile test data from impact machine is compared with stress-strain data from the INSTRON servo-hydraulic testing machine with DIC for different strain rates. Close matching in elastic modulus, yield strength, tensile strength, and elongation are observed. Material parameters of a strain rate-dependent material model (modified J-C model) are extracted from drop weight impact testing machine data clubbed with other tensile test data, used in FE simulation of very high strain rate tensile tests, and validated with experimental results. Later, the same material model and material parameters are used to simulate Charpy impact tests at various velocities and compared with experimental results which also show close matching.

Prediction of skull fractures in blunt force head traumas using finite element head models.

Traumatic head injuries remain a leading cause of death and disability worldwide. Although skull fractures are one of the most common head injuries, the fundamental mechanics of cranial bone and its impact tolerance are still uncertain. In the present study, a strain-rate-dependent material model for cranial bone has been proposed and implemented in subject-specific Finite Element (FE) head models in order to predict skull fractures in five real-world fall accidents. The subject-specific head models were developed following an established image-registration-based personalization pipeline. Head impact boundary conditions were derived from accident reconstructions using personalized human body models. The simulated fracture lines were compared to those visible in post-mortem CT scans of each subject. In result, the FE models did predict the actual occurrence and extent of skull fractures in all cases. In at least four out of five cases, predicted fracture patterns were comparable to ones from CT scans and autopsy reports. The tensile material model, which was tuned to represent rate-dependent tensile data of cortical skull bone from literature, was able to capture observed linear fractures in blunt indentation loading of a skullcap specimen. The FE model showed to be sensitive to modeling parameters, in particular to the constitutive parameters of the cortical tables. Nevertheless, this study provides a currently lacking strain-rate dependent material model of cranial bone that has the capacity to accurately predict linear fracture patterns. For the first time, a procedure to reconstruct occurrences of skull fractures using computational engineering techniques, capturing the all-in-all fracture initiation, propagation and final pattern, is presented.

A Strain Rate Dependent Damage Model for Evaluating the Dynamic Response of CFRTP Laminates with Different Stacking Sequence

Carbon fiber reinforced thermoplastic polymer (CFRTP) laminates can be used in packaging electronics components to reduce weight and shield external disturbance. The CFRTP structures in operation are inevitably to suffer dynamic loading conditions such as falling rocks, tools and impacts. In this study, a strain rate dependent material model for accurately evaluating the dynamic response of CFRTP laminates with different stacking sequence was proposed. The model was composed of three components: a strain rate dependent constitute model, a strain rate related damage initiation model and an energy-based damage evolution model. The strain rate effect of modulus and strength was described by a stacking sequence related matrix, and the damage initiation model could describe the matrix, fiber and delamination damage of CFRTP laminates without introducing cohesive elements. The material model was implemented into finite element software ABAQUS by user defines subroutine VUMAT. The low velocity impact tests of CFRTP laminates with quasi-isotropic and angle-ply stacking sequence were used to provide validation data. The dynamic response of CFRTP laminates from numerical results were highly consistent with the experimental results. The mechanical response of CFRTP laminates were affected by stacking sequence and impact energy, and the numerical error of proposed material model significantly decreased with the increasing impact energy especially for the laminae with damage occur.

Ballistic penetration simulation of a 3D woven fabric using high strain-rate dependent yarn model

3D woven fabric has great application potential in military armor systems. Here we report numerical simulation of 3 D angle interlock woven fabric(3DAWF) subjected to the ballistic impact using LS-DYNA. We employed membrane elements to construct the mesoscale yarn-level 3DAWF model to improve computational efficiencies and accuracy. The simplified Johnson-Cook (SJC) material model was proposed for simulating yarns' dynamic behaviors under high-speed impact loadings. The SJC material model and commonly used strain-rate dependent material model Cowper-Symonds (CS) were taken into the FEA model to simulate the fabric's ballistic impact behaviors separately. The ballistic impact tests of 3DAWF subjected to the Full Metal Jacket (FMJ) projectile under the strike velocity 190 ∼ 320 m/s were carried out to validate the new material model. Comparing the results between the tests and theoretical model found that the FEA model using the SJC material model can accurately predict projectile's residual velocities and fabric's deformation and damages. The numerical model using SJC yarn constitutive models can precisely capture the impact mechanism of 3DAWF.

Identification of the LLDPE Constitutive Material Model for Energy Absorption in Impact Applications.

Current industrial trends bring new challenges in energy absorbing systems. Polymer materials as the traditional packaging materials seem to be promising due to their low weight, structure, and production price. Based on the review, the linear low-density polyethylene (LLDPE) material was identified as the most promising material for absorbing impact energy. The current paper addresses the identification of the material parameters and the development of a constitutive material model to be used in future designs by virtual prototyping. The paper deals with the experimental measurement of the stress-strain relations of linear low-density polyethylene under static and dynamic loading. The quasi-static measurement was realized in two perpendicular principal directions and was supplemented by a test measurement in the 45° direction, i.e., exactly between the principal directions. The quasi-static stress-strain curves were analyzed as an initial step for dynamic strain rate-dependent material behavior. The dynamic response was tested in a drop tower using a spherical impactor hitting a flat material multi-layered specimen at two different energy levels. The strain rate-dependent material model was identified by optimizing the static material response obtained in the dynamic experiments. The material model was validated by the virtual reconstruction of the experiments and by comparing the numerical results to the experimental ones.

A strain rate dependent nonlinear elastic orthotropic model for SFRC structures

A strain rate dependent orthotropic model for steel fiber reinforced concrete (SFRC) structures subjected to impact or blast loads is proposed in this paper. Based on the previously introduced orthotropic model for plain concrete, an improved strain rate dependent material model for SFRC is developed to account for the effect derived from the addition of steel fibers in the concrete matrix and to cope with the multiaxial strain rate dependent behavior of SFRC. In addition to verification of the constructed multiaxial strength envelope of SFRC through correlations with experimental data, improved failure strains in the uniaxial stress-strain relation are also introduced to minimize the mesh size dependency in the numerical results. Finally, the proposed orthotropic model is incorporated into LS-DYNA as a user defined material model. Numerical analyses were performed for experiments of RC and SFRC slabs under projectile impact and blast loading, and the obtained results show that the addition of the steel fibers provides a considerable improvement in the structural resistance and the proposed model effectively simulates the structural responses of SFRC structures while minimizing the mesh size dependency in the numerical results.

Dynamic behaviors and protection mechanisms of sulcata tortoise carapace

This paper presents the compressive behavior of tortoise carapace at high strain rates and its protection mechanisms under impact loading. Both experimental and numerical results are reported. Tortoise is a land-based desert-dwelling animal taxonomically classified in the order of Testudines. The carapace is the dome-shaped upper part of the tortoise shell that protects its body from predator attacks. The carapace structure is composed of four layers formed as a composite structure with a porous core. The outer surface is keratin scutes made of fibrous structural proteins. The remaining layers are bone-like materials which are dorsal cortex, cancellous interior and ventral cortex. The compressive behavior at high rate of deformation is examined using split Hopkinson pressure bar (SHPB) technique. The results shown in the stress-strain plot illustrate a strain-rate hardening effect. The impact test is conducted using a gas gun with 6.35-mm diameter steel bearing balls as projectiles. The responses of carapace sample under a range of impact velocities are investigated to analyze its protection mechanisms. The numerical model of impact test is created to obtain an insight into mechanical behaviors of the carapace structure that cannot be observed in the experiments. The strain rate dependent material model is defined based on the SHPB test results. The distributions of stress and rebound velocity are presented and discussed.

Numerical investigation of high velocity impact on foam-filled honeycomb structures including foam fracture model

An appropriate finite element model is developed to simulate the high velocity impact of projectiles on polyurethane foam filled aluminum honeycomb. First, the numerical model of the high velocity impact of the projectiles on the empty aluminum honeycomb is developed using a strain rate dependent material model. A VUMAT subroutine including two different fracture criteria proposed by researchers is developed. The fracture criterion that shows similar behavior to experimental observations, is selected. The numerical model of the projectiles impact on the foam-filled honeycomb is compared with available experimental results, and the ballistic limit velocities are predicted with good accuracy.

Influence of velocity on high-temperature fundamental abrasive contact: A numerical and experimental approach

In some forming industrial applications, hot steel components leave the rolling train with speeds ranging from 1 to 10 m/s, sliding against fixed components. Scratching of the surface is often inevitable, especially in presence of hard oxides. The experimental assessment of this tribosystem is highly challenging since scratch experiments are typically carried out at velocities two or even three orders of magnitude slower. The severe discrepancy between strain rates in laboratory and field application poses serious concerns in the transferability of the obtained results. To cover the high-speed range of the application, experimental high-temperature tests were combined with numerical high-temperature scratch simulations on ferrite at various scratching velocities between 1 m/s and 10 m/s. A strain-rate dependent material model was used and parameterized to fit uniaxial tensile tests at 800 °C. Material point method simulations using the open-source particle code LAMMPS confirmed the trends found with experimental scratch data. According to the numerical simulations, the velocity effect on the scratch depth is reduced with increasing velocity. A remarkable velocity effect was also identified experimentally in the range of 10 mm/min – 10 mm/s with up to 50% less scratch depth at higher velocities.

Improvement of axial forging process for spline shaft by die design

As an effective method of forming spline shaft, the axial cold forging process is appropriate for long shaft and exhibits high efficiency. The two defects of folds and accumulation were found to result in large forming force and low quality of products in the experiments. To analyse the cause the defects, a finite element model was built with a strain rate-dependent material model, in which the parameters were determined by material test. Metal flow was divided into three different parts, and relevant parameters were proposed to quantify them. An assembling method of three dies and a new die with a variable tooth shape were designed by the fast simulated annealing optimization method using the quantification parameters to improve metal flow and decrease forming force. The differences in metal flow, tooth profile and axial force were compared amongst conventional axial forging, the assembling dies and the new die. The assembling method of three dies decreased the force by 31.2% compared with the conventional axial forging. However, fold defects were significant which might lead to stress concentration. On the basis of the optimisation of the assembling method, the die with a variable tooth shape decreased the load by 55% compared with the conventional axial forging. The shape quality of the product formed by the new die with a variable tooth width was also improved owing to the avoidance of defects.

Characterization of Stress-Strain Behavior of Superplastic Titanium Alloy by Free Bulging Tests with Pressure Jumps

The work is dedicated to determination of stress-strain behavior of Ti6Al4V alloy deformed in conditions of biaxial tension provided by free bulging testing. The dome height during each test was continuously measured and recorded using a magnetostrictive position transducer. All the tests were performed using stepped pressure regime with jump pressure changing between two values at evenly spaced time moments. This experimental technique provides the possibility to study strain rate sensitivity index variation during the test and subsequently construct strain and strain rate dependent material model. The output data of each test include the evolution of dome height, subsequent pressure regime and final thickness of the specimen at the dome pole. In the framework of this study the processing of such data in order to evaluate the material behavior is discussed. Inverse analysis with different material models was implemented as well as special direct technique allowing one to construct stress-strain curves based on the results of free bulging tests with pressure jumps. The obtained material model was verified by finite element simulation.

Modeling and experimental validation of friction self-piercing riveted aluminum alloy to magnesium alloy

Friction self-piercing riveting (F-SPR) process has been proposed to achieve crack-free joining of low-ductility materials by combining SPR process with the concept of friction stir processing. The inhibition of cracking in an F-SPR joint is related to the in-process temperature as well as plastic deformation of materials, which are controlled by the process parameters, i.e., spindle speed and feed rate. However, the relationship between F-SPR process parameters and the temperature characteristics within the joint has not been established. In the current study, a coupled thermal-mechanical model based on solid mechanics was setup to study the F-SPR process of aluminum alloy and magnesium alloy. Temperature and strain rate-dependent material models and preset crack surface method were integrated in the model and geometry comparisons were conducted for model validation. Based on this model, the evolutions of temperature and plastic deformation in the rivet and the sheets of an F-SPR joint were obtained to reveal the formation mechanism of the joint. The temperature distribution and evolution of the sheet materials were correlated with F-SPR process parameters, and a critical spinning speed of 2000 rpm at a feed rate of 1.35 mm/s was determined capable of inhibiting cracking in the magnesium sheet.

Material Characterization and Low Cycle Fatigue Model of Low Ag Content Lead-Free Solder

In this paper, a method of design-for-reliability for the advanced electronic package under temperature cycling (TC) condition is demonstrated, including material characterization, reliability test, finite element analysis (FEA), and fatigue life model development. Tensile tests are conducted for Sn–1.0Ag–0.5Cu–0.02Ni (SAC105Ni0.02) solder alloy at four stain rates of $10^{{-5}}$ , $10^{{-4}}$ , $10^{{-3}}$ , and $10^{{-2}}$ and four test temperatures of − 35°C, 25 °C, 75 °C, and 125 °C to develop temperature- and strain rate-dependent material models. Tensile creep tests are carried out at various temperatures and stress levels to study creep behavior. TC reliability test is conducted for ball grid array package with SAC105Ni0.02 solder joints. Thermal fatigue lives are obtained from TC test with different failure rates. FEA simulation is carried out for each package using the developed mechanical properties and creep model of the solder. Fatigue life models with different failure rates are proposed for the SAC105Ni0.02 solder by combining simulation results and experimental data. Fatigue resistance of the SAC105Ni0.02 solder is comparable with that of high Ag content SAC solders.

Residual stress state induced by high frequency mechanical impact treatment in different steel grades – Numerical and experimental study

High frequency mechanical impact treatment is observed to increase the fatigue strength of welded joints. This technique induces compressive residual stresses, increases the local hardness, and reduces the stress concentration by modifying the weld toe radius. The goal of this study was to investigate residual stresses induced by ultrasonic impact treatment in S355, S700MC, and S960 grades steel experimentally and numerically. Plate specimens were manufactured and treated with different treatment intensities i.e. vibration amplitudes of the Sonotrode. The indentation depths were measured by the aid of a laser scanner and residual stresses using X-ray diffraction technique. The effect of steel grade and treatment intensity on the induced compressive residual stress state was firstly studied experimentally. In addition, displacement controlled simulations were carried out to estimate the local residual stress condition considering the effect of different material models. Both the numerically estimated and experimentally measured residual stresses were qualitatively in good agreement. Residual stress state in S355 and S700MC can be estimated well using combined strain rate dependent material model. No significant effect of the treatment intensity is observed on the indentation depth and residual stress state for S355 grade steel. The indentation depth decreases with the increase in the yield strength of the steel.

Numerical evaluation of cohesive zone models for modeling impact induced delamination in composite materials

This paper compares four cohesive zone models for modeling delamination caused by impact on composite materials. The four cohesive zone models differ by the way rate-dependent material properties, such as strength and fracture toughness, are treated. The influence of the cohesive zone model formulation on the prediction of delamination size is evaluated using the numerical example of a dynamic punch test. It is demonstrated that the use of strain-rate dependent material models significantly influences the numerical result. It is also shown that both, the rate-dependent strength and the rate-dependent fracture toughness, must be considered.

Modelling and solvability of a class steady-state metal-forming problems

Abstract For a class of steady-state metal-forming problems, with rigid-plastic, incompressible, strain-rate dependent material model and with unilateral contact and nonlocal Coulomb’s frictional boundary conditions, a variational inequality formulation is derived and by proving the convergence of a modified secant-modulus method, existence and uniqueness results are obtained. A finite element - modified secant-modulus computational algorithm is developed and applied for solving illustrative problems.

NUMERICAL SIMULATIONS OF QUASI-STATIC INDENTATION AND LOW VELOCITY IMPACT OF ROHACELL 51 WF FOAM

Numerical simulations of quasi-static indentation and low velocity impact of low density polymethacrylimide (PMI) Rohacell 51 WF foam using indenters with different nose shapes (conical, truncated-conical, hemi-spherical and flat) were carried out using the finite element code LS-DYNA. A 2D axisymmetric model was generated. A strain-rate dependent material model and r-adaptive remeshing were used for low velocity impact simulations. Numerical predictions matched the available experimental data very well. Moreover, the predicted resistance force closely matched the empirical results. The results demonstrated the ability of the model to reproduce the deformation mechanisms of the penetration process of Rohacell 51 WF foam.

Dynamic Characterization of CFRP Composite Materials – Toward a Pre-normative Testing Protocol – Application to T700GC/M21 Material

The lack of normalized protocols to perform dynamic material tests could lead to inconsistent results compared to normalized static tests ones, or between different dynamic test campaigns. Such inconsistencies may be problematic when an accurate identification of strain rate dependent material models is needed, from creep to fast dynamics loadings. For instance, changes in the dynamic specimen in-plane geometry compared to the normalized static ones proved to influence the apparent elastic modulus of CFRP materials. In the present work, a pre-normative study of the dynamic specimen geometry is presented. First, a geometrical criterion is proposed for the [+/-45]s specimens that are commonly used (Rosen tension tests) to study the shear behaviour of composite materials, in order to answer the above mentioned consistency issue between static and dynamic test results. Then, several biases are pointed out which appear when using the (various) normative static test exploitation rules to identify the material properties from dynamic test results, which end up to the proposal of general recommendations to calculate CFRP elastic apparent modulus the same and accurate way for static and dynamic tests, and identify advanced visco-elastic models.

Development of a strain rate dependent material model of human cortical bone for computer-aided reconstruction of injury mechanisms

Computer-aided methods such as finite-element simulation offer a great potential in the forensic reconstruction of injury mechanisms. Numerous studies have been performed on understanding and analysing the mechanical properties of bone and the mechanism of its fracture. Determination of the mechanical properties of bones is made on the same basis used for other structural materials. The mechanical behaviour of bones is affected by the mechanical properties of the bone material, the geometry, the loading direction and mode and of course the loading rate. Strain rate dependency of mechanical properties of cortical bone has been well demonstrated in literature studies, but as many of these were performed on animal bones and at non-physiological strain rates it is questionable how these will apply in the human situations. High strain-rates dominate in a lot of forensic applications in automotive crashes and assault scenarios. There is an overwhelming need to a model which can describe the complex behaviour of bone at lower strain rates as well as higher ones. Some attempts have been made to model the viscoelastic and viscoplastic properties of the bone at high strain rates using constitutive mathematical models with little demonstrated success. The main objective of the present study is to model the rate dependent behaviour of the bones based on experimental data. An isotropic material model of human cortical bone with strain rate dependency effects is implemented using the LS-DYNA material library.We employed a human finite element model called THUMS (Total Human Model for Safety), developed by Toyota R&D Labs and the Wayne State University, USA. The finite element model of the human femur is extracted from the THUMS model. Different methods have been employed to develop a strain rate dependent material model for the femur bone. Results of one the recent experimental studies on human femur have been employed to obtain the numerical model for cortical femur. A forensic application of the model is explained in which impacts to the arm have been reconstructed using the finite element model of THUMS. The advantage of the numerical method is that a wide range of impact conditions can be easily reconstructed. Impact velocity has been changed as a parameter to find the tolerance levels of injuries to the lower arm. The method can be further developed to study the assaults and the injury mechanism which can lead to severe traumatic injuries in forensic cases.

A Rate Dependent Stress-Strain Relationship Model for Normal, High and Ultra-High Strength Concrete

High and ultra-high strength concrete are becoming popular for many applications, including critical infrastructure subjected to high strain rate loading such as blast and impact. A strain rate dependent material model that is applicable to a range of strengths, varying from normal strength to ultra-high strength concrete, is presented in this paper. The results from a comprehensive experimental study conducted to investigate the strength and deformation capacity of concrete cylinders under high-velocity impact loading using a Split Hopkinson Pressure Bar (SHPB) test setup is reported. Unconfined 50 mm diameter concrete cylinders with compressive strengths varying from 32 MPa (4640 psi) to 160 MPa (23 200 psi) were tested to derive the dynamic properties of concrete at strain rates up to 300 s−1. The SHPB test data were analysed to obtain the stress-strain relationships and strength dynamic increase factors (DIFs) for these concrete specimens under dynamic axial compression.