A Numerical Study on Ductile Failure of Porous Ductile Solids With Rate-Dependent Matrix Behavior

2019 ◽  
Vol 87 (3) ◽  
Author(s):  
Lars Edvard Blystad Dæhli ◽  
David Morin ◽  
Tore Børvik ◽  
Ahmed Benallal ◽  
Odd Sture Hopperstad
Keyword(s):  
Finite Element ◽  
Strain Rate ◽  
Strain Localization ◽  
Ductile Failure ◽  
Unit Cell ◽  
Strain Rates ◽  
Proportional Loading ◽  
Loading Paths ◽  
Rate Dependent ◽  
Constitutive Formulation

Abstract This work examines the effects of loading rate on the plastic flow and ductile failure of porous solids exhibiting rate-dependent behavior relevant to many structural metals. Two different modeling approaches for ductile failure are employed and numerical analyses are performed over a wide range of strain rates. Finite element unit cell simulations are carried out to evaluate the macroscopic mechanical response and ductile failure by void coalescence for various macroscopic strain rates. The unit cell results are then used to assess the accuracy of a rate-dependent porous plasticity model, which is subsequently used in strain localization analyses based on the imperfection band approach. Strain localization analyses are conducted for (i) proportional loading paths and (ii) non-proportional loading paths obtained from finite element simulations of axisymmetric and flat tensile specimens. The effects of strain rate are most apparent on the stress–strain response, whereas the effects of strain rate on ductile failure is found to be small for the adopted rate-dependent constitutive model. However, the rate-dependent constitutive formulation tends to regularize the plastic strain field when the strain rate increases. In the unit cell simulations, this slightly increases the strain at coalescence with increasing strain rate compared to a rate-independent constitutive formulation. When the strain rate is sufficiently high, the strain at coalescence becomes constant. The strain localization analyses show a negligible effect of strain rate under proportional loading, while the effect of strain rate is more pronounced when non-proportional loading paths are assigned.

scholarly journals Dynamic constitutive relation of 5083P-O aluminium alloy and its influence on energy-absorbing structure

2018 ◽  
Vol 10 (10) ◽  
pp. 168781401880733
Author(s):  
Yue Feng ◽  
Shoune Xiao ◽  
Bing Yang ◽  
Tao Zhu ◽  
Guangwu Yang ◽  
...  
Keyword(s):  
Finite Element ◽  
Strain Rate ◽  
Aluminium Alloy ◽  
Constitutive Relation ◽  
High Strain ◽  
Deformation Mode ◽  
Strain Rates ◽  
Strengthening Effect ◽  
Element Simulation ◽  
Energy Absorbing

Dynamic and quasi-static tensile tests of 5083P-O aluminium alloy were carried out using RPL100 electronic creep/fatigue testing machine and the split Hopkinson tension bar, respectively. The dynamic constitutive relation of the material at high strain rates was studied, and the constitutive model in accordance with Cowper–Symonds form was established. At the same time, a method to describe the constitutive relation of material using the strain rate interpolation method which is included in LS-DYNA software was proposed. The advantages and accuracy of this method were verified by comparing the results of the finite element simulation with the fitting results of the Cowper-Symonds model. The influence of material strain rate effect on squeezing force, energy absorption and deformation mode of the squeezing energy-absorbing structure based on the constitutive models of 5083P-O were studied by means of finite element simulation. The results show that when the strain rate of the structure deformation is low, the material strain rate strengthening effect has little influence on the structure. However, with the increase of the strain rate, the strengthening effect of the material will improve the squeezing force and the energy absorption of the structure, and will also influence the deformation mode, that is, the decrease of the deformation with high strain rates while the increase of the deformation with low strain rates.

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.

scholarly journals Strain-Rate-Dependent Deformation Behavior and Mechanical Properties of a Multi-Phase Medium-Manganese Steel

Metals ◽  
2019 ◽  
Vol 9 (3) ◽  
pp. 344 ◽  
Author(s):  
Simon Sevsek ◽  
Christian Haase ◽  
Wolfgang Bleck
Keyword(s):  
Mechanical Properties ◽  
Strain Rate ◽  
Strain Rate Sensitivity ◽  
Deformation Behavior ◽  
Rate Sensitivity ◽  
Manganese Steel ◽  
Strain Rates ◽  
Rate Dependent ◽  
Medium Manganese Steel ◽  
Multi Phase

The strain-rate-dependent deformation behavior of an intercritically annealed X6MnAl12-3 medium-manganese steel was analyzed with respect to the mechanical properties, activation of deformation-induced martensitic phase transformation, and strain localization behavior. Intercritical annealing at 675 °C for 2 h led to an ultrafine-grained multi-phase microstructure with 45% of mostly equiaxed, recrystallized austenite and 55% ferrite or recovered, lamellar martensite. In-situ digital image correlation methods during tensile tests revealed strain localization behavior during the discontinuous elastic-plastic transition, which was due to the localization of strain in the softer austenite in the early stages of plastic deformation. The dependence of the macroscopic mechanical properties on the strain rate is due to the strain-rate sensitivity of the microscopic deformation behavior. On the one hand, the deformation-induced phase transformation of austenite to martensite showed a clear strain-rate dependency and was partially suppressed at very low and very high strain rates. On the other hand, the strain-rate-dependent relative strength of ferrite and martensite compared to austenite influenced the strain partitioning during plastic deformation, and subsequently, the work-hardening rate. As a result, the tested X6MnAl12-3 medium-manganese steel showed a negative strain-rate sensitivity at very low to medium strain rates and a positive strain-rate sensitivity at medium to high strain rates.

Investigation of the axial compressive behavior of Kevlar fibers using the dynamic loop test

2019 ◽  
Vol 89 (18) ◽  
pp. 3825-3838
Author(s):  
Ahmad Abuobaid ◽  
Raja Ganesh ◽  
John W Gillespie
Keyword(s):  
Strain Rate ◽  
High Speed ◽  
Failure Strain ◽  
Kink Band ◽  
Test Method ◽  
Strain Rates ◽  
Compressive Failure ◽  
Band Formation ◽  
Rate Dependent ◽  
Strain And Strain Rate

A dynamic loop test method for measuring strain rate-dependent fiber properties was developed. During dynamic loop testing, the fiber ends are accelerated at constant levels of 20.8, 50 and 343 m/s2. The test method is used to study Kevlar® KM2-600, which fails in axial compression due to kink band formation. The compressive failure strain and strain rate at the onset of kink band formation is calculated from the critical loop diameter ( D C), which is monitored throughout the test using a high-speed camera. The results showed that compressive failure strain increases with strain rates from quasi-static to a maximum strain rate of 116 s−1 by a factor of ∼3. Kink angles (φ) and kink band spacing ( D S) were 60 ° ± 2 ° and 16 ± 3 μm, respectively, over the strain rates tested. Rate-dependent mechanisms of compressive failure by kink band formation were discussed.

Constitutive Modeling of a Thermoplastic Olefin Over a Broad Range of Strain Rates

2006 ◽  
Vol 128 (4) ◽  
pp. 551-558 ◽  
Author(s):  
Yan Wang ◽  
Ellen M. Arruda
Keyword(s):  
Strain Rate ◽  
Strain Hardening ◽  
Three Dimensional ◽  
Elastic Response ◽  
Strain Rates ◽  
Strain Behavior ◽  
Rate Dependent ◽  
State Dependent ◽  
Deformation State ◽  
Ann Arbor

A microstructually motivated, three-dimensional, large deformation, strain rate dependent constitutive model has been developed for a semi-crystalline, blended, thermoplastic olefin (TPO) (Wang, Y., 2002, Ph.D. thesis, The University of Michigan, Ann Arbor, MI). Various experiments have been conducted to characterize the TPO and to verify the modeling approach (Wang, Y., 2002, Ph.D. thesis, The University of Michigan, Ann Arbor, MI). The model includes a quantitative rate-dependent Young’s modulus, a nonlinear viscoelastic response between initial linear elastic response and yield due to inherent microstructural irregularity, rate and temperature dependent yield with two distinctive yield mechanisms for low and high strain rates, temperature-dependent strain hardening, plastic deformation of crystalline regions, and adiabatic heating. It has been shown to accurately capture the observed TPO stress-strain behavior including the rate-dependent initial linear elastic response; temperature, strain rate, and deformation state-dependent yield; temperature and deformation state-dependent strain hardening; and pronounced thermal softening effects at high (impact) strain rates. The model has also been examined for its ability to predict the response in plane strain compression based on material parameters chosen to capture the uniaxial compression response. The model is predictive of the initial strain rate dependent stiffness, yield, and strain hardening responses in plane strain. Such predictive capability demonstrates the versatility with which this model captures the three-dimensional anisotropic nature of TPO stress-strain behavior.

scholarly journals Inelastic Behavior in Repeated Shearing of Bovine White Matter

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
Taylor S. Cohen ◽  
Andrew W. Smith ◽  
Panagiotis G. Massouros ◽  
Philip V. Bayly ◽  
Amy Q. Shen ◽  
...  
Keyword(s):  
White Matter ◽  
Strain Rate ◽  
Critical Strain ◽  
Mechanical Response ◽  
Tissue Mechanics ◽  
Strain Rates ◽  
Inelastic Behavior ◽  
Fiber Breakage ◽  
Rate Dependent ◽  
Strain Threshold

Understanding the brain’s response to multiple loadings requires knowledge of how straining changes the mechanical response of brain tissue. We studied the inelastic behavior of bovine white matter and found that when this tissue is stretched beyond a critical strain threshold, its reloading stiffness drops. An upper bound for this strain threshold was characterized, and was found to be strain rate dependent at low strain rates and strain rate independent at higher strain rates. Results suggest that permanent changes to tissue mechanics can occur at strains below those believed to cause physiological disruption or rupture of axons. Such behavior is characteristic of disentanglement in fibrous-networked solids, in which strain-induced mechanical changes may result from fiber realignment rather than fiber breakage.

Strain Rate Effects and Rate-Dependent Constitutive Models of Lead-Based and Lead-Free Solders

2009 ◽  
Vol 77 (1) ◽  
Author(s):  
Fei Qin ◽  
Tong An ◽  
Na Chen
Keyword(s):  
Strain Rate ◽  
Impact Analysis ◽  
Solder Joints ◽  
High Strain ◽  
Drop Impact ◽  
Lead Free ◽  
Strain Rates ◽  
High Strain Rates ◽  
Rate Dependent ◽  
Lead Free Solders

As traditional lead-based solders are banned and replaced by lead-free solders, the drop impact reliability is becoming increasingly crucial because there is little understanding of mechanical behaviors of these lead-free solders at high strain rates. In this paper, mechanical properties of one lead-based solder, Sn37Pb, and two lead-free solders, Sn3.5Ag and Sn3.0Ag0.5Cu, were investigated at strain rates that ranged from 600 s−1 to 2200 s−1 by the split Hopkinson pressure and tensile bar technique. At high strain rates, tensile strengths of lead-free solders are about 1.5 times greater than that of the Sn37Pb solder, and also their ductility are significantly greater than that of the Sn37Pb. Based on the experimental data, strain rate dependent Johnson–Cook models for the three solders were derived and employed to predict behaviors of solder joints in a board level electronic package subjected to standard drop impact load. Results indicate that for the drop impact analysis of lead-free solder joints, the strain rate effect must be considered and rate-dependent material models of lead-free solders are indispensable.

scholarly journals Strain rate dependent plasticity and fracture of DP1000 steel under proportional and non-proportional loading

2021 ◽  
pp. 104446
Author(s):  
Sarath Chandran ◽  
Wenqi Liu ◽  
Junhe Lian ◽  
Sebastian Münstermann ◽  
Patricia Verleysen
Keyword(s):  
Strain Rate ◽  
Proportional Loading ◽  
Dependent Plasticity ◽  
Rate Dependent

scholarly journals FE Analysis of Critical Testing Parameters in Kolsky Bar Experiments for Elastomers at High Strain Rate

Materials ◽  
2019 ◽  
Vol 12 (23) ◽  
pp. 3817
Author(s):  
Chaudhry ◽  
Czekanski
Keyword(s):  
Finite Element ◽  
High Strain Rate ◽  
Strain Rate ◽  
Pulse Shaping ◽  
High Strain ◽  
Kolsky Bar ◽  
Specimen Geometry ◽  
Strain Rates ◽  
Butadiene Rubber ◽  
Testing Apparatus

The main aim of this research is to present complete methodological guidelines for dynamic characterization of elastomers when subjected to strain rates of 100/s–10,000/s. We consider the following three aspects: (i) the design of high strain rate testing apparatus, (ii) finite element analysis for the optimization of the experimental setup, and (iii) experimental parameters and validation for the response of an elastomeric specimen. To test low impedance soft materials, design of a modified Kolsky bar is discussed. Based on this design, the testing apparatus was constructed, validated, and optimized numerically using finite element methods. Furthermore, investigations on traditional pulse shaping techniques and a new design for pulse shaper are described. The effect of specimen geometry on the homogeneous deformation has been thoroughly accounted for. Using the optimized specimen geometry and pulse shaping technique, nitrile butadiene rubber was tested at different strain rates, and the experimental findings were compared to numerical predictions.

Dynamic Fracture of Natural Rubber3

2007 ◽  
Vol 35 (4) ◽  
pp. 252-275 ◽  
Author(s):  
Ali A. Al-Quraishi ◽  
Michelle S. Hoo Fatt
Keyword(s):  
Finite Element ◽  
Carbon Black ◽  
Natural Rubber ◽  
Strain Rate ◽  
Fracture Energy ◽  
Dynamic Fracture ◽  
High Strain ◽  
Field Strain ◽  
Far Field ◽  
Strain Rates

Abstract This paper illustrates how the fracture energy of a tensile strip made of unfilled and 25 phr carbon black-filled natural rubber varies with far-field strain rate in the range 0.01–71 s−1. Quasistatic and dynamic fracture tests were performed at room temperature with an electromechanical INSTRON machine, a servo-hydraulic MTS machine, and Charpy tensile apparatus, respectively. It was found that the fracture energy of the unfilled natural rubber did not vary significantly over the range of sample strain rate, but there was significant variation in the fracture energy of the 25 phr carbon black-filled natural rubber from 0.01 to 71 s−1 sample strain rate. The fracture energy of the 25 phr carbon black-filled natural rubber at a sample strain rate of 0.1 s−1 was about three times greater than it was at the 10 s−1 sample strain rate. While the carbon black fillers increased the fracture energy of natural rubber by about 200% at quasistatic sample strain rates (0.01–0.1 s−1) and at 71 s−1, the carbon black fillers did nothing to improve the fracture energy of natural rubber at sample strain rates between 5 and 29 s−1. In this strain rate range, the fracture energy of 25 phr carbon black-filled natural rubber was almost the same as that in the unfilled natural rubber. The variation in the fracture energy with far-field strain rate was due to changes in the material behavior of natural rubber at high strain rates. Finite element analysis using a high-strain-rate constitutive equation for the 25 phr carbon black rubber specimen was used to calculate the fracture energy of the specimen at a sample strain rate of 55 s−1, and good agreement was found between the test and finite element results.

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