An Alternative Decomposition of the Strain Gradient Tensor

2001 ◽  
Vol 69 (2) ◽  
pp. 139-141 ◽  
Author(s):  
H. Jiang ◽  
Y. Huang ◽  
T. F. Guo ◽  
K. C. Hwang
Keyword(s):  
Strain Gradient ◽  
Strain Field ◽  
Numerical Study ◽  
Volumetric Strain ◽  
Crack Tip ◽  
Square Root ◽  
Crack Tip Field ◽  
Gradient Tensor ◽  
Classical Plasticity ◽  
Square Root Singularity

An alternative decomposition of the strain gradient tensor is proposed in this paper in order to ensure that the deviatoric strain gradient vanishes for an arbitrary volumetric strain field, which is consistent with the physical picture of plastic deformation. The theory of mechanism-based strain gradient (MSG) plasticity is then modified accordingly based on this new decomposition. The numerical study of the crack-tip field based on the new theory shows that the crack tip in MSG plasticity has the square-root singularity, and the stress level is much higher than the HRR field in classical plasticity.

scholarly journals Effect of microstructure on fatigue crack tip field of laser melting deposited Ti–5Al–5Mo–5V–1Cr–1Fe titanium alloy

2018 ◽  
Vol 165 ◽  
pp. 02009
Author(s):  
Kai Wang ◽  
Rui Bao ◽  
Siyuan Ren ◽  
Dong Liu ◽  
Chuliang Yan
Keyword(s):  
Titanium Alloy ◽  
Fatigue Crack ◽  
Strain Field ◽  
Crack Tip ◽  
Image Correlation ◽  
Laser Melting ◽  
Crack Tip Field ◽  
Significant Difference ◽  
Microstructure Effect ◽  
Effect Of Microstructure

In this paper, experimental and simulated investigations were carried out to understand the effect of microstructure on the fatigue crack tip strain field of laser melting deposited Ti–5Al–5Mo–5V–1Cr–1Fe titanium alloy. The mechanical properties of the laser melting deposited material corresponding to different microstructure zones were measured by digital image correlation method under in-situ static stretching, and the results indicate that the direction of primary α lamellas has great influence on the mechanical property of each grain. The crack tip strain fields considering the influence of material microstructure under constant amplitude conditions were measured, and the strain field of plastic zone has significant difference. Crystal plasticity finite element simulation of the static tensile and crack tip field considering the microstructure effect had been conducted and compare with experiment results. The simulation results are in good agreement with the test results in both the static tension strain field and crack tip strain field.

Crack tip field andJ-integral with strain gradient effect

2004 ◽  
Vol 20 (3) ◽  
pp. 228-237 ◽  
Author(s):  
Xia Song ◽  
Wang Tzuchiang ◽  
Chen Shaohua
Keyword(s):  
Strain Gradient ◽  
Crack Tip ◽  
Crack Tip Field ◽  
Gradient Effect

Analysis of Crack Tip Field in Materials with Creep Behavior

2012 ◽  
Vol 525-526 ◽  
pp. 297-300
Author(s):  
Qing Hua Meng ◽  
Wen Yan Liang ◽  
Zhen Qing Wang
Keyword(s):  
Effective Stress ◽  
Creep Behavior ◽  
Strain Field ◽  
Crack Tip ◽  
Mode I ◽  
Stress And Strain ◽  
Crack Tip Field ◽  
Asymptotic Equations ◽  
Growing Crack

The stress and strain field near the tip of Mode I growing crack in materials under creep conditions is examined. The case of the effective stress equal to zero is considered. The asymptotic equations for the crack of the crack tip field are derived and solved numerically. It is concluded that the rates of stress and strain posses the rδ-1 singularity near the tip crack, and the stresses remain finite at the crack tip.

scholarly journals Unconventional singularities and energy balance in frictional rupture

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Efim A. Brener ◽  
Eran Bouchbinder
Keyword(s):  
Energy Balance ◽  
Square Root ◽  
Earthquake Physics ◽  
Macroscopic Theory ◽  
Scale Separation ◽  
Rate Dependent ◽  
Theoretical Predictions ◽  
Spatially Extended ◽  
Singularity Order ◽  
Square Root Singularity

AbstractA widespread framework for understanding frictional rupture, such as earthquakes along geological faults, invokes an analogy to ordinary cracks. A distinct feature of ordinary cracks is that their near edge fields are characterized by a square root singularity, which is intimately related to the existence of strict dissipation-related lengthscale separation and edge-localized energy balance. Yet, the interrelations between the singularity order, lengthscale separation and edge-localized energy balance in frictional rupture are not fully understood, even in physical situations in which the conventional square root singularity remains approximately valid. Here we develop a macroscopic theory that shows that the generic rate-dependent nature of friction leads to deviations from the conventional singularity, and that even if this deviation is small, significant non-edge-localized rupture-related dissipation emerges. The physical origin of the latter, which is predicted to vanish identically in the crack analogy, is the breakdown of scale separation that leads an accumulated spatially-extended dissipation, involving macroscopic scales. The non-edge-localized rupture-related dissipation is also predicted to be position dependent. The theoretical predictions are quantitatively supported by available numerical results, and their possible implications for earthquake physics are discussed.

Scale-Dependent Crack Modeling for Investigation the Effect of Geometrically Necessary Dislocations in Micro/Nano Grain Size of Copper

2016 ◽  
Vol 15 ◽  
pp. 1-16 ◽  
Author(s):  
Amin Zaami ◽  
Ali Shokuhfar
Keyword(s):  
Grain Size ◽  
Stress Concentration ◽  
Strain Gradient ◽  
Stress Concentration Factor ◽  
Size Effects ◽  
Crack Tip ◽  
Length Scale ◽  
State Variables ◽  
Dependent Model ◽  
Homogeneous Strain

In this study, a scale-dependent model is employed to investigate the size effects of copper on the behavior of the crack-tip. This model includes the homogeneous and non-homogeneous strain hardening based on the wavelet interpretation of size effect. Introducing additional micro/nano structural considerations together with decreasing grain size, different size effects can be obtained. As the size dependency is not taken into account in conventional plasticity, an enhanced theory which is related to the strain gradient introduces a length scale will give more realistic representations of state variables near the crack-tip. Accordingly, the contribution of geometrically necessary dislocations (GNDs) activity on strengthening and stress concentration factor is identified in the crack-tip. Finally, the affected zone which is dominated by presence of GNDs is identified

VARIATIONAL MULTISCALE ANALYSIS OF SOLIDS WITH STRAIN GRADIENT PLASTIC EFFECTS USING MESHFREE APPROXIMATION

2005 ◽  
Vol 02 (04) ◽  
pp. 601-626 ◽  
Author(s):  
JEOUNG-HEUM YEON ◽  
SUNG-KIE YOUN
Keyword(s):  
Strain Gradient ◽  
Partition Of Unity ◽  
Meshfree Method ◽  
Internal Variable ◽  
Plasticity Theory ◽  
Fine Scale ◽  
Meshfree Approximation ◽  
Gradient Effect ◽  
Classical Plasticity ◽  
Variational Form

A meshfree multiscale method is presented for efficient analysis of solids with strain gradient plastic effects. In the analysis of strain gradient plastic solids, localization due to increased hardening of strain gradient effect appears. Chen-Wang theory is adopted, as a strain gradient plasticity theory. It represents strain gradient effects as an internal variable and retains the essential structure of classical plasticity theory. In this work, the scale decomposition is carried out based on variational form of the problem. Coarse scale is designed to represent global behavior and fine scale to represent local behavior and gradient effect by using the intrinsic length scale. From the detection of high strain gradient region, fine scale region is adopted. Each scale variable is approximated using meshfree method. Meshfree approximation is well suited for adaptivity. As a method of increasing resolution, partition of unity based extrinsic enrichment is used. Each scale problem is solved iteratively. The proposed method is applied to bending of a thin beam and bimaterial shear layer and micro-indentation problems. Size effects can be effectively captured in the results of the analysis.

Mismatch Effect on the Mixed Mode Type Creep Crack within Weldment

2016 ◽  
Vol 853 ◽  
pp. 281-285
Author(s):  
Jun Hui Zhang ◽  
Yan Wei Dai
Keyword(s):  
Mixed Mode ◽  
Stress Triaxiality ◽  
Crack Tip ◽  
Crack Tip Field ◽  
Creep Crack ◽  
Loading Mode ◽  
The Difference ◽  
Engineering Practices ◽  
Mismatch Effect ◽  
Transient And Steady State

Creep crack within weldments are very common in engineering practices, and the cracking location in these welding structures always appears at the HAZ location. The mismatch effect on the mixed mode creep crack is still not clear in these available literatures. The aim of this paper is to investigate the mismatch influence on the creep crack of mixed mode thoroughly. A mixed mode creep crack within HAZ is established in this paper. The leading factor that dominates the creep crack tip field under mixed loading mode is studied. The influences of mismatch effect on mode mixity, stress distribution and stress triaxiality are proposed. The difference of mixed mode creep crack and normal mode I or mode II creep crack are compared. The influence of mixity factor on the transient and steady state creep of crack tip are also analyzed.

INVESTIGATIONS ON THE DYNAMIC NEAR-CRACK-TIP FIELD USING THE GRID METHOD

1988 ◽  
Vol 49 (C3) ◽  
pp. C3-307-C3-312
Author(s):  
K. KUSSMAUL ◽  
T. DEMLER ◽  
A. KLENK
Keyword(s):  
Crack Tip ◽  
Grid Method ◽  
Crack Tip Field
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