scholarly journals Investigation of Density- and Strain Rate-dependent Strain Hardening-softening-coupled material Behavior of Polyurethane Foams using Elasto-viscoplastic Constitutive Model

2020 ◽  
Vol 58 (5) ◽  
pp. 357-367
Author(s):  
Tae-Rim Kim ◽  
Chi-Seung Lee
Keyword(s):  
Constitutive Model ◽  
Strain Rate ◽  
Strain Hardening ◽  
Material Behavior ◽  
Implicit Time ◽  
Stress Strain ◽  
Integration Algorithm ◽  
Material Response ◽  
Material Parameters ◽  
Rate Dependent

Polyurethane foam (PUF) is one of the most well-known cellular materials and is widely employed in various industrial and biomedical fields thanks to its many advantages. These include mechanical and material characteristics such as low density and thermal conductivity, and high specific elastic modulus and strength. Despite of these advantages, the PUF has extremely complex material nonlinearity, with changes in density and strain rate, which is a major obstacle to material design and the application of PUF-based structures. PUF has elasto-viscoplastic behavior including three stages of material features, linear elasticity, softening/plateau with stress drop and densification. These phenomena depend strongly on strain rate and density. Therefore, in this study, a phenomenological constitutive model, namely, an elasto-viscoplastic model, was proposed to describe the density- and strain rate-dependent material nonlinear behavior of PUF. The yield surface-independent plastic multiplier, and the hardening- and softening-associated internal state variables proposed by Frank and Brockman, and Zairi et al. were adopted in the constitutive model, respectively. The proposed constitutive model was discretized using the implicit time integration algorithm and was implemented into a user-defined subroutine of the commercial finite element analysis program, ABAQUS. At the same time, a deterministic identification method for material parameters of the constitutive model was introduced to predict the precise material response of PUF under arbitrary densities and strain rates. To do this, the three-dimensional constitutive model was contracted to a one-dimensional equation, and the explicit equation for each material parameter was derived. Then, the strain hardening- and softeningdependent material parameters were calculated using experimental results, such as the work hardening ratestress curve and the yield stress-strain rate curve. After analyzing the obtained material parameters, it was found that the material parameters were strongly dependent on the density and the strain rate. Consequently, the macroscopic material response of PUF, such as a uniaxial compressive stress-strain curve, can be predicted based on the proposed method in this study.

A full-range stress-strain model for metallic materials depicting non-linear strain-hardening behavior

2020 ◽  
pp. 030932472095779
Author(s):  
Digendranath Swain ◽  
S Karthigai Selvan ◽  
Binu P Thomas ◽  
Ahmedul K Asraff ◽  
Jeby Philip
Keyword(s):  
Constitutive Model ◽  
Strain Hardening ◽  
Image Correlation ◽  
Linear Strain ◽  
Stress Strain ◽  
Material Parameters ◽  
Hardening Behavior ◽  
Non Linear ◽  
Strain Hardening Behavior ◽  
Strain Model

Ramberg-Osgood (R-O) type stress-strain models are commonly employed during elasto-plastic analysis of metals. Recently, 2-stage and 3-stage R-O variant models have been proposed to replicate stress-strain behavior under large plastic deformation. The complexity of these models increases with the addition of each stage. Moreover, these models have considered deformation till necking only. In this paper, a simplistic multi-stage constitutive model is proposed to capture the strain-hardening non-linearity shown by metals including its post necking behavior. The constitutive parameters of the proposed stress-strain model can be determined using only elastic modulus and yield strength. 3-D digital image correlation was used as an experimental tool for measuring full-field strains on the specimens, which were subsequently utilized to obtain the material parameters. Our constitutive model is demonstrated with an aerospace-grade stainless steel AISI 321 wherein deformation response averaged over the gauge length (GL) and at a local necking zone are compared. The resulting averaged and local material parameters obtained from the proposed model provide interesting insights into the pre and post necking deformation behavior. Our constitutive model would be useful for characterizing highly ductile metals which may or may not depict non-linear strain hardening behavior including their post necking deformations.

scholarly journals Transformation of Test Data for the Specification of a Viscoelastic Marlow Model

Solids ◽  
2020 ◽  
Vol 1 (1) ◽  
pp. 2-15
Author(s):  
Olaf Hesebeck
Keyword(s):  
Tensile Test ◽  
Strain Rate ◽  
Finite Strain ◽  
Strain Curve ◽  
Model Parameters ◽  
Strain Rates ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Material Response ◽  
Rate Dependent

The combination of hyperelastic material models with viscoelasticity allows researchers to model the strain-rate-dependent large-strain response of elastomers. Model parameters can be identified using a uniaxial tensile test at a single strain rate and a relaxation test. They enable the prediction of the stress–strain behavior at different strain rates and other loadings like compression or shear. The Marlow model differs from most hyperelastic models by the concept not to use a small number of model parameters but a scalar function to define the mechanical properties. It can be defined conveniently by providing the stress–strain curve of a tensile test without need for parameter optimization. The uniaxial response of the model reproduces this curve exactly. The coupling of the Marlow model and viscoelasticity is an approach to create a strain-rate-dependent hyperelastic model which has good accuracy and is convenient to use. Unfortunately, in this combination, the Marlow model requires to specify the stress–strain curve for the instantaneous material response, while experimental data can be obtained only at finite strain rates. In this paper, a transformation of the finite strain rate data to the instantaneous material response is derived and numerically verified. Its implementation enables us to specify hyperelastic materials considering strain-rate dependence easily.

An Analysis of the Split Hopkinson Bar Technique for Strain-Rate-Dependent Material Behavior

1973 ◽  
Vol 40 (1) ◽  
pp. 277-282 ◽  
Author(s):  
T. Nicholas
Keyword(s):  
Strain Rate ◽  
Numerical Procedure ◽  
Hopkinson Bar ◽  
Material Behavior ◽  
Stress Strain ◽  
Torsional Mode ◽  
Split Hopkinson Bar ◽  
Rate Dependent ◽  
Split Hopkinson ◽  
Prestressed Materials

The analysis of the split Hopkinson bar experiment for determining dynamic material behavior is examined for several specific examples of specimen materials which exhibit strain-rate-dependent mechanical behavior. The torsional mode of deformation is chosen as more closely representing a one-dimensional state of stress. Details of the propagation and reflection of stress waves within the specimen are studied using a numerical procedure based on the method of characteristics. Reconstituted stress-strain curves calculated from the conventional analysis of the split Hopkinson bar experiment are compared with actual material behavior for several simulated experiments involving variations in input stress, gage length, material behavior, and static stress-strain curves including statically prestressed materials. The validity of the experimental technique is discussed and limitations on its use are delineated.

Dynamic Compression Behavior and Numerical Modeling of Ti-6246 Alloy at Different Temperatures

2012 ◽  
Vol 527 ◽  
pp. 159-164 ◽  
Author(s):  
Dmitri Gomon ◽  
Mikko Hokka ◽  
Veli Tapani Kuokkala
Keyword(s):  
Numerical Modeling ◽  
Strain Rate ◽  
Strain Hardening ◽  
High Strain ◽  
Material Behavior ◽  
Materials Testing ◽  
Strain Rates ◽  
High Strain Rates ◽  
Stress Strain ◽  
Strain Hardening Rate

The current research concentrates on the characterization of the mechanical behavior of Ti-6Al-2Sn-4Zr-6Mo alloy. The material was studied in compression using the Split Hopkinson Pressure Bar (SHPB) equipment at high strain rates and conventional servohydraulic materials testing devices at low strain rates. The tests were performed at temperatures ranging from room temperature up to 600 °C. According to the results of the compression tests, the strain hardening rate of the studied material decreases strongly with increasing strain rate. The observed strong decrease in the strain hardening rate with increasing strain rate is a consequence of the extremely strong adiabatic heating of the material due to its high strength and low thermal conductivity. In this study, the Johnson-Cook material model parameters were obtained from isothermal stress-strain curves that were calculated from the experimental (adiabatic) stress-strain data. In this paper, the results of the mechanical testing at high strain rates and the numerical modeling of the material behavior are presented and discussed in details.

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

Polymers ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1537
Author(s):  
Luděk Hynčík ◽  
Petra Kochová ◽  
Jan Špička ◽  
Tomasz Bońkowski ◽  
Robert Cimrman ◽  
...  
Keyword(s):  
Strain Rate ◽  
Material Model ◽  
Low Density Polyethylene ◽  
Low Density ◽  
Linear Low Density Polyethylene ◽  
Stress Strain ◽  
Rate Dependent ◽  
Constitutive Material Model ◽  
Principal Directions ◽  
Constitutive Material

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.

scholarly journals Strain Rate Dependent Ductility and Strain Hardening in Q&P Steels

2021 ◽  
Author(s):  
Christopher B. Finfrock ◽  
Melissa M. Thrun ◽  
Diptak Bhattacharya ◽  
Trevor J. Ballard ◽  
Amy J. Clarke ◽  
...  
Keyword(s):  
Strain Rate ◽  
Strain Hardening ◽  
Rate Dependent

Generation of Cyclic Stress-Strain Curves for Sheet Metals

2000 ◽  
Author(s):  
K. M. Zhao ◽  
J. K. Lee
Keyword(s):  
Constitutive Model ◽  
Kinematic Hardening ◽  
Optimization Procedure ◽  
High Strength ◽  
Cyclic Stress ◽  
Bending Moments ◽  
Sheet Metals ◽  
Stress Strain ◽  
Normal Anisotropy ◽  
Material Parameters

Abstract The main objective of this paper is to generate cyclic stress-strain curves for sheet metals so that the springback can be simulated accurately. Material parameters are identified by an inverse method within a selected constitutive model that represents the hardening behavior of materials subjected to a cyclic loading. Three-point bending tests are conducted on sheet steels (mild steel and high strength steel). Punch stroke, punch load, bending strain and bending angle are measured directly during the tests. Bending moments are then computed from these measured data. Bending moments are also calculated based on a constitutive model. Normal anisotropy and nonlinear isotropic/kinematic hardening are considered. Material parameters are identified by minimizing the normalized error between two bending moments. Micro genetic algorithm is used in the optimization procedure. Stress-strain curves are generated with the material parameters found in this way, which can be used with other plastic models.

Energy absorption behaviour of different grades of steel sheets using a strain rate dependent constitutive model

2017 ◽  
Vol 111 ◽  
pp. 9-18 ◽  
Author(s):  
Pundan K. Singh ◽  
Anindya Das ◽  
S. Sivaprasad ◽  
Pinaki Biswas ◽  
Rahul K. Verma ◽  
...  
Keyword(s):  
Constitutive Model ◽  
Strain Rate ◽  
Energy Absorption ◽  
Steel Sheets ◽  
Rate Dependent

scholarly journals Extension of Flow Behaviour and Damage Models for Cast Iron Alloys with Strain Rate Effect

2020 ◽  
Author(s):  
Chuang Liu ◽  
Dongzhi Sun ◽  
Xianfeng Zhang ◽  
Florence Andrieux ◽  
Tobias Gerster
Keyword(s):  
Cast Iron ◽  
Constitutive Model ◽  
Strain Rate ◽  
Mechanical Behavior ◽  
Damage Model ◽  
Iron Alloys ◽  
Strain Rate Range ◽  
Strain Rates ◽  
Damage Models ◽  
Rate Dependent

Abstract Cast iron alloys with low production cost and quite good mechanical properties are widely used in the automotive industry. To study the mechanical behavior of a typical ductile cast iron (GJS-450) with nodular graphite, uni-axial quasi-static and dynamic tensile tests at strain rates of 10− 4, 1, 10, 100, and 250 s− 1 were carried out. In order to investigate the effects of stress state, specimens with various geometries were used in the experiments. Stress–strain curves and fracture strains of the GJS-450 alloy in the strain-rate range of 10− 4 to 250 s− 1 were obtained. A strain rate-dependent plastic flow law based on the Voce model is proposed to describe the mechanical behavior in the corresponding strain-rate range. The deformation behavior at various strain rates is observed and analyzed through simulations with the proposed strain rate-dependent constitutive model. The available damage model from Bai and Wierzbicki is extended to take the strain rate into account and calibrated based on the analysis of local fracture strains. The validity of the proposed constitutive model including the damage model was verified by the corresponding experimental results. The results show that the strain rate has obviously nonlinear effects on the yield stress and fracture strain of GJS-450 alloys. The predictions with the proposed constitutive model and damage models at various strain rates agree well with the experimental results, which illustrates that the rate-dependent flow rule and damage models can be used to describe the mechanical behavior of cast iron alloys at elevated strain rates.

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