Fracture Toughness of Structural Steels as a Function of the Rate Parameter T ln A/ε˙

1967 ◽  
Vol 89 (1) ◽  
pp. 86-92 ◽  
Author(s):  
H. T. Corten ◽  
A. K. Shoemaker
Keyword(s):  
Fracture Toughness ◽  
Strain Rate ◽  
High Strain ◽  
Initial Crack ◽  
Structural Steels ◽  
Structure Design ◽  
Strain Rates ◽  
Rate Parameter ◽  
Service Conditions ◽  
Temperature Strain

The influence of temperature and strain rate upon the fracture toughness of structural steel is the question considered in this paper. The hypothesis is proposed that fracture toughness, KIc, for initial crack extension is a single-valued function of the rate parameter T ln A/ε˙. Measurements made by Krafft and Sullivan of fracture toughness, KIc, for three steels covering a range of low temperatures and high strain rates are presented as a function of this rate parameter. Two of the materials support the contention that a single-valued relation exists between KIc and the parameter, while scatter in the data for the third steel does not allow a conclusion. The complexity of design against fracture in structural steels is reviewed. For conservative design it must be assumed that a crack is present in the structure. Design against fracture must insure that the minimum fracture toughness at the service temperature, strain rate and stress is sufficient to prevent this crack from extending rapidly through the base metal. A means of using low temperature laboratory fracture toughness tests for estimating a minimum fracture toughness corresponding to the service conditions is discussed.

Hot Deformation Resistance of an AA5083 Alloy under High Strain Rate

2014 ◽  
Vol 626 ◽  
pp. 553-560
Author(s):  
Shi Rong Chen ◽  
Chung Yung Wu ◽  
Yi Liang Ou ◽  
Yen Liang Yeh
Keyword(s):  
High Strain Rate ◽  
Strain Rate ◽  
Hot Deformation ◽  
High Strain ◽  
Load Cell ◽  
Deformation Resistance ◽  
Strain Rates ◽  
Flow Curves ◽  
Aa5083 Alloy ◽  
Temperature Strain

Axisymmetric compression tests using Gleeble 3800 simulator were carried out to investigate hot deformation behaviors of an AA5083 alloy under high strain rate conditions. Sharp temperature rise and load cell ringing characterized by severely vibrational load responses were encountered at strain rates higher than 20 s-1 and sample buckling occurred at low temperatures. The load cell ringing was corrected using a moving average method with a two-way filtering operation to correct phase distortion. Isothermal flow curves were obtained by fitting the instantaneous temperatures into a binomial function, while buckling was correlated with sample height and Young’s modulus. After the corrections, hyperbolic sine equation was successfully used to extend from the hot tensile data having strain rates lower than 3 s-1 to 100 s-1. Quantitative analyses were accordingly made over the effects of temperature, strain rate and work hardening behavior on the flow curves. The previous constitutive equation in form of temperature, strain and strain rate was modified to predict the hot deformation resistance of the AA5083 alloy at temperatures of 250-450oC under the high strain rate operations.

High Strain Rate Fracture Behavior of Sn-Ag-Cu Solder Joints on Cu Substrates

2011 ◽  
Author(s):  
Z. Huang ◽  
P. Kumar ◽  
I. Dutta ◽  
J. H. L. Pang ◽  
R. Sidhu ◽  
...  
Keyword(s):  
Fracture Toughness ◽  
Yield Strength ◽  
Strain Rate ◽  
Fracture Mechanism ◽  
Fracture Behavior ◽  
Solder Joints ◽  
High Strain ◽  
Effective Thickness ◽  
Strain Rates ◽  
Cu Substrates

During service, micro-cracks form inside solder joints, making a microelectronic package prone to failure particularly during a drop. Hence, the understanding of the fracture behavior of solder joints under drop conditions, synonymously at high strain rates and in mixed mode, is critically important. This study reports: (i) the effects of processing conditions (reflow parameters and aging) on the microstructure and fracture behavior of Sn-3.8%Ag-0.7%Cu (SAC387) solder joints attached to Cu substrates, and (ii) the effects of the loading conditions (strain rate and loading angle) on the fracture toughness of these joints, especially at high strain rates. A methodology for calculating critical energy release rate, GC, was employed to quantify the fracture toughness of the joints. Two parameters, (i) effective thickness of the interfacial intermetallic compounds (IMC) layer, which is proportional to the product of the thickness and the roughness of the IMC layer, and (ii) yield strength of the solder, which depends on the solder microstructure and the loading rate, were identified as the dominant quantities affecting the fracture behavior of the solder joints. The fracture toughness of the solder joint decreased with an increase in the effective thickness of the IMC layer and the yield strength of the solder. A 2-dimensional fracture mechanism map with the effective thickness of the IMC layer and the yield strength of the solder as two axes and the fracture toughness as well as the fraction of different fracture paths as contour-lines was prepared. Trends in the fracture toughness of the solder joints and their correlation with the fracture modes are explained using the fracture mechanism map.

Dynamic Deformation Behavior of As-Extruded Mg-Gd-Y Magnesium Alloy and the Microstructural Evolution

2011 ◽  
Vol 284-286 ◽  
pp. 1579-1583
Author(s):  
Ping Li Mao ◽  
Zheng Liu ◽  
Chang Yi Wang ◽  
Feng Wang
Keyword(s):  
Magnesium Alloy ◽  
Strain Rate ◽  
Deformation Behavior ◽  
High Strain ◽  
Split Hopkinson Pressure Bar ◽  
Dynamic Deformation ◽  
Strain Rates ◽  
Compression Axis ◽  
Deformation Localization ◽  
Dynamic Deformation Behavior

The dynamic deformation behavior of an as-extruded Mg-Gd-Y magnesium alloy was studied by using Split Hopkinson Pressure Bar (SHPB) apparatus under high strain rates of 102 s-1 to 103s-1 in the present work, in the mean while the microstructure evolution after deformation were inspected by OM and SEM. The results demonstrated that the material is not sensitive to the strain rate and with increasing the strain rate the yield stress of as-extruded Mg-Gd-Y magnesium alloy has a tendency of increasing. The microstructure observation results shown that several deformation localization areas with the width of 10mm formed in the strain rates of 465s-1 and 2140s-1 along the compression axis respectively, and the grain boundaries within the deformation localization area are parallel with each other and are perpendicular to the compression axis. While increasing the strain rate to 3767s-1 the deformation seems become uniform and all the grains are compressed flat in somewhat. The deformation mechanism of as-extruded Mg-Gd-Y magnesium alloy under high strain rate at room temperature was also discussed.

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 Effect of the Strain Rate on the Fracture Behaviour of High Pressure Pre-Charged Samples

Proceedings ◽  
2018 ◽  
Vol 2 (23) ◽  
pp. 1417
Author(s):  
Guillermo Álvarez Díaz ◽  
Tomás Eduardo García Suárez ◽  
Cristina. Rodríguez González ◽  
Francisco Javier Belzunce Varela
Keyword(s):  
Fracture Toughness ◽  
High Pressure ◽  
Hydrogen Embrittlement ◽  
Strain Rate ◽  
Fracture Behaviour ◽  
Structural Steels ◽  
Gaseous Hydrogen ◽  
Displacement Rate ◽  
Steel Strength ◽  
Fracture Tests

The aim of this work is to study the effect of the displacement rate on the hydrogen embrittlement of two different structural steels grades used in energetic applications. With this purpose, samples were pre-charged with gaseous hydrogen at 19.5 MPa and 450 °C for 21 h. Then, fracture tests of the pre-charged specimens were performed, using different displacement rates. It is showed that the lower is the displacement rate and the largest is the steel strength, the strongest is the reduction of the fracture toughness due to the presence of internal hydrogen.

Impact tensile behavior and frequency response of 3D braided composites

2011 ◽  
Vol 82 (3) ◽  
pp. 280-287 ◽  
Author(s):  
Xuehui Gan ◽  
Jianhua Yan ◽  
Bohong Gu ◽  
Baozhong Sun
Keyword(s):  
High Strain Rate ◽  
Strain Rate ◽  
Tensile Properties ◽  
High Strain ◽  
Tensile Modulus ◽  
Tensile Failure ◽  
Uniaxial Tensile ◽  
Strain Rates ◽  
Braided Composites ◽  
3D Braided Composites

The uniaxial tensile properties of 4-step 3D braided E-glass/epoxy composites under quasi-static and high-strain rate loadings have been investigated to evaluate the tensile failure mode at different strain rates. The uniaxial tensile properties at high strain rates from 800/s to 2100/s were tested using the split Hopkinson tension bar (SHTB) technique. The tensile properties at quasi-static strain rate were also tested and compared with those in high strain rates. Z-transform theory is applied to 3D braided composites to characterize the system dynamic behaviors in frequency domain. The frequency responses and the stability of 3D braided composites under quasi-static and high-strain rate compression have been analyzed and discussed in the Z-transform domain. The results indicate that the stress-strain curves are rate sensitive, and tensile modulus, maximum tensile stress and corresponding tensile strain are also sensitive to the strain rate. The tensile modulus, maximum tensile stress of the 3D braided composites are linearly increased with the strain rate. With increasing of the strain rate (from 0.001/s to 2100/s), the tensile failure of the 3D braided composite specimens has a tendency of transition from ductile failure to brittle failure. The magnitude response and phase response is very different in quasi-static loading with that in high-strain rate loading. The 3D braided composite system is more stable at high strain rate than quasi-static loading.

Research on Numerical Algorithm of Constitutive Equation under High Speed Deformation in Hadfield Steel

2012 ◽  
Vol 562-564 ◽  
pp. 688-692 ◽  
Author(s):  
Deng Yue Sun ◽  
Jing Li ◽  
Fu Cheng Zhang ◽  
Feng Chao Liu ◽  
Ming Zhang
Keyword(s):  
High Strain Rate ◽  
Strain Rate ◽  
Deformation Behavior ◽  
High Speed ◽  
High Strain ◽  
Equivalent Stress ◽  
Hadfield Steel ◽  
Stress And Strain ◽  
Strain Rates ◽  
The Finite Element Method

The influence of the strain rate on the plastic deformation of the metals was significant during the high strain rate of loading. However, it was very difficult to obtain high strain rate data (≥ 104 s-1) by experimental techniques. Therefore, the finite element method and iterative method were employed in this study. Numerical simulation was used to characterise the deformation behavior of Hadfield steel during explosion treatment. Base on experimental data, a modified Johnson-Cook equation for Hadfield steel under various strain rate was fitted. The development of two field variables was quantified during explosion hardening: equivalent stress and strain rates.

A Dynamic Mechanical Analysis of T2 Copper at High Strain Rates

2019 ◽  
Vol 812 ◽  
pp. 38-44
Author(s):  
Shuai Chen ◽  
Wen Bin Li ◽  
Xiao Ming Wang ◽  
Wen Jin Yao
Keyword(s):  
Yield Strength ◽  
Strain Rate ◽  
High Strain ◽  
Split Hopkinson Pressure Bar ◽  
Pure Copper ◽  
Dislocation Slip ◽  
Strain Rates ◽  
High Strain Rates ◽  
Stress Strain ◽  
Shpb Test

This work compares the pure copper (T2 copper)’s stress-strain relationship at different strain rates in the uni-axial tension test and Split Hopkinson Pressure Bar (SHPB) test. Small samples were utilized in the high strain rate SHPB test in which the accuracy was modified by numerical simulation. The experimental results showed that the T2 copper’s yield strength at high strain rates largely outweighed the quasi static yield strength. The flow stress in the stress-strain curves at different strain rates appeared to be divergent and increased with the increase in strain rates, showing great strain strengthening and strain rate hardening effects. Metallographic observation showed that the microstructure of T2 copper changed from equiaxed grains to twins and the interaction between the dislocation slip zone grain boundary and twins promoted the super plasticity distortion in T2 copper.

Numerical Simulation of Hot High Strain Rate Torsion Tests for Al-Based Alloys

2019 ◽  
Vol 822 ◽  
pp. 66-71
Author(s):  
Anton Naumov ◽  
Anatolii Borisov ◽  
Anastasiya Y. Doroshchenkova
Keyword(s):  
Numerical Simulation ◽  
High Strain Rate ◽  
Strain Rate ◽  
Visual Analysis ◽  
Physical Simulation ◽  
High Strain ◽  
Torsion Test ◽  
Strain Rates ◽  
Deform 3D

The present research describes the comparison of numerical and physical simulation of hot high strain rate torsion tests for Al-based alloys in order to clarify the accuracy of calculations using basic grades of materials in Deform-3DTM software. A comparative visual analysis of the results is presented. Obtained data on the distribution of temperatures, strains, stresses and strain rates during the torsion test are discussed.

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