Statistical Volume Elements for the Characterization of Angle-Dependent Fracture Strengths in Anisotropic Microcracked Materials

2020 ◽  
Vol 6 (2) ◽  
Author(s):  
Justin M. Garrard ◽  
Reza Abedi
Keyword(s):  
Fracture Strength ◽  
Computational Cost ◽  
Spatial Inhomogeneity ◽  
Uniaxial Tensile ◽  
Anisotropic Rock ◽  
Linear Elastic ◽  
Covariance Functions ◽  
Macroscopic Fracture ◽  
Elastic Fracture

Abstract Statistical volume elements (SVEs) are used to homogenize fracture strength of rock, based on the microcrack statistics of a real-world Yuen-Long marble sample. The small size of SVEs enables maintaining inhomogeneities in fracture properties with lower computational cost compared to methods that explicitly model microcracks at macroscale. Maintaining inhomogeneity is important to capture realistic fracture patterns in rock as a quasi-brittle material. Uniaxial tensile, uniaxial compressive, and shear strengths are derived for arbitrary angle for loading and orientation of a single crack by using the linear elastic fracture mechanics (LEFM) method and incorporating frictional effects. Mesoscopic fracture strength fields are generated for different strengths and angle of loading by traversing the spatial domain with circular SVEs. Increasing the SVE size smoothens the spatial inhomogeneity and angular anisotropy of homogenized strengths. Spatial and angular covariance functions of the random fields are obtained to demonstrate how fracture strength varies in space and by changing the angle of loading. Two isotropic and anisotropic rock domains are studied and shown to have very different single- and two-point statistics. Macroscopic fracture simulations by an asynchronous spacetime discontinuous Galerkin (aSDG) method demonstrate that most macroscopic cracks for the anisotropic domain are aligned with the weakest strength planes.

Statistical Volume Elements for the Characterization of Angle-Dependent Fracture Strengths

2018 ◽  
Author(s):  
Justin M. Garrard ◽  
Reza Abedi ◽  
Philip L. Clarke
Keyword(s):  
Fracture Strength ◽  
Random Fields ◽  
Cross Correlation ◽  
Rock Fracture ◽  
Uniaxial Tensile ◽  
Uniaxial Tensile Strength ◽  
Element Size ◽  
Macroscopic Fracture ◽  
Shed Light

The fracture response of rock, a quasi-brittle material, is very sensitive to its microstructural defects. Herein, we use statistical volume elements (SVEs) to characterize rock fracture strength at the mesoscale, based on the distribution of microcracks at the microscale. The use of SVEs ensures that the material randomness is maintained upon “averaging” of microscale features. Certain fracture strengths, such as uniaxial tensile strength, uniaxial hydrostatic strength, shear strength, and uniaxial compressive strength, are obtained and characterized for different angles of loading. Thus, a material with anisotropic fracture strength can be characterized. Statistics of the characterized strengths are analyzed, as well as their auto- and cross-correlation functions of these random fields to shed light on the length scales, relative to the volume element size, at which homogenized properties vary. While crack interaction is not included, the analysis provides insight on the distribution and correlation of different strengths. Finally, the asynchronous spacetime discontinuous Galerkin method is used for macroscopic fracture analyses of two rock domains homogenized by SVEs.

Characterization of Elevated Temperature Crack Growth in Hastelloy-X Using Integral Parameters

1995 ◽  
Vol 117 (3) ◽  
pp. 299-304 ◽  
Author(s):  
K. S. Kim ◽  
R. H. Van Stone
Keyword(s):  
Crack Growth ◽  
Elevated Temperatures ◽  
Growth Data ◽  
Hastelloy X ◽  
Linear Elastic ◽  
Acceptable Accuracy ◽  
Elastic Fracture ◽  
Crack Growth Rates ◽  
Temperature Crack

Linear elastic fracture mechanics approaches are not suitable for prediction of fatigue crack growth in the nonlinear regime at elevated temperatures. The objective of this paper is to investigate the ability of the integral parameters by Blackburn (J*), by Kishimoto et al. (Jˆ), and by Atluri et al. (ΔTp*, ΔTp) to correlate crack growth data of Hastelloy-X at elevated temperatures under nominally elastic and nominally plastic loading. Crack growth is analyzed using a finite element method, and the integral parameters are computed from the results of analysis. The experimental crack growth rates are correlated with these parameters. It is found that J*, Jˆ, and ΔTp* can correlate crack growth data within an acceptable accuracy.

Experimental Characterization of the Elastic-Plastic Strain Fields at the Crack Tip Due to Cyclic Loading

1994 ◽  
Vol 116 (2) ◽  
pp. 187-192 ◽  
Author(s):  
N. Ranganathan ◽  
K. Jendoubi ◽  
N. Merah
Keyword(s):  
Cyclic Loading ◽  
Plastic Strain ◽  
Crack Tip ◽  
High Strength ◽  
Elastic Plastic ◽  
Strain Behavior ◽  
Linear Elastic ◽  
Elastic Fracture ◽  
Aluminum Alloy 2024

Some mechanical components cease to function satisfactorily, failing either under excessive elastic deformation or extensive plastic yielding. In the case of constrained plastification, the researcher is faced with some difficulties in evaluating plastic and elastic-plastic strain behavior near the crack tip. In the present study local strains are measured by microstrain gages, mounted near the crack tip on CT specimens made from the high strength aluminum alloy 2024-T351 under cyclic loading at constant ΔK. The behavior and the evolution of the elastic-plastic zone are studied as a function of the stress ratio R, the thickness of the specimen and the level of ΔK. The experimental results are compared with those given by numerical and theoretical analyses based on the concepts of linear elastic fracture mechanics (LEFM).

scholarly journals Influence of the Test Configuration and Temperature on the Mechanical Behaviour of WC-Co

Metals ◽  
2020 ◽  
Vol 10 (3) ◽  
pp. 322
Author(s):  
Luis M. González ◽  
Ernesto Chicardi ◽  
Francisco J. Gotor ◽  
Raul Bermejo ◽  
Luis Llanes ◽  
...  
Keyword(s):  
Mechanical Strength ◽  
Mechanical Behaviour ◽  
Cemented Carbides ◽  
Mechanical Degradation ◽  
Test Configuration ◽  
Linear Elastic ◽  
Four Point Bending ◽  
Macroscopic Fracture ◽  
Elastic Fracture ◽  
Weibull Theory

In this work, the effect of the test configuration and temperature on the mechanical behaviour of cemented carbides (WC-Co) with different carbide grain sizes (dWC) and cobalt volume fractions (VCo), implying different binder mean free paths (λCo), was studied. The mechanical strength was measured at 600 °C with bar-shaped specimens subjected to uniaxial four-point bending (4PB) tests and with disc specimens subjected to biaxial ball-on-three-balls (B3B) tests. The results were analysed within the frame of the Weibull theory and compared with strength measurements performed at room temperature under the same loading conditions. A mechanical degradation greater than 30% was observed when the samples were tested at 600 °C due to oxidation phenomena, but higher Weibull moduli were obtained as a result of narrower defect size distributions. A fractographic analysis was conducted with broken specimens from each test configuration. The number of fragments (Nf) and the macroscopic fracture surface were related to the flexural strength and fracture toughness of WC-Co. For a given number of fragments, higher mechanical strength values were always obtained for WC-Co grades with higher KIc. The observed differences were discussed based on a linear elastic fracture mechanics (LEFM) model, taking into account the effect of the temperature and microstructure of the cemented carbides on the mechanical strength.

scholarly journals Linear Elastic Fracture Mechanics Characterization of an Anisotropic Shale

2018 ◽  
Vol 8 (1) ◽  
Author(s):  
Y. Luo ◽  
H. P. Xie ◽  
L. Ren ◽  
R. Zhang ◽  
C. B. Li ◽  
...  
Keyword(s):  
Fracture Mechanics ◽  
Linear Elastic Fracture Mechanics ◽  
Linear Elastic ◽  
Elastic Fracture

Fatigue Failure Analysis Using the Theory of Critical Distance

2011 ◽  
Vol 462-463 ◽  
pp. 663-667 ◽  
Author(s):  
Ruslizam Daud ◽  
Ahmad Kamal Ariffin ◽  
Shahrum Abdullah ◽  
Al Emran Ismail
Keyword(s):  
Stress Concentration ◽  
Fatigue Failure ◽  
Notch Root ◽  
High Stress ◽  
Critical Distance ◽  
Future Research ◽  
Element Analysis ◽  
Linear Elastic ◽  
The Finite Element Analysis ◽  
Elastic Fracture

This paper explores the initial potential of theory of critical distance (TCD) which offers essential fatigue failure prediction in engineering components. The intention is to find the most appropriate TCD approach for a case of multiple stress concentration features in future research. The TCD is based on critical distance from notch root and represents the extension of linear elastic fracture mechanics (LEFM) principles. The approach is allowing possibilities for fatigue limit prediction based on localized stress concentration, which are characterized by high stress gradients. Using the finite element analysis (FEA) results and some data from literature, TCD applications is illustrated by a case study on engineering components in different geometrical notch radius. Further applications of TCD to various kinds of engineering problems are discussed.

Investigation on Stress and Strain Singularity in LEFM

2006 ◽  
Vol 306-308 ◽  
pp. 31-36
Author(s):  
Zheng Yang ◽  
Wanlin Guo ◽  
Quan Liang Liu
Keyword(s):  
High Stress ◽  
Crack Tip ◽  
Plane Stress State ◽  
Stress And Strain ◽  
Linear Elastic ◽  
Geometrical Nonlinear ◽  
Maximum Crack ◽  
Elastic Fracture ◽  
Plain Strain ◽  
Strain Singularity

Stress and strain singularity at crack-tip is the characteristic of Linear Elastic Fracture Mechanics (LEFM). However, the stress, strain and strain energy at crack-tip may be infinite promoting conflicts with linear elastic hypothesis. It is indicated that the geometrical nonlinear near the crack-tip should not be neglected for linear elastic materials. In fact, the crack-tip blunts under high stress and strain, and the singularity vanishes due to the deformation of crack surface when loading. The stress at crack-tip may still be very high even though the singularity vanishes. The low bound of maximum crack-tip stress is the modulus of elastic in plane stress state, while in plain strain state, it is greater than the modulus of elastic, and will increase with the Poisson’s ratio.

A New Specimen for Measuring the Interfacial Toughness of Al-0.5%Cu Thin Film on Si Substrate

2005 ◽  
Vol 297-300 ◽  
pp. 521-526
Author(s):  
Insu Jeon ◽  
Masaki Omiya ◽  
Hirotsugu Inoue ◽  
Kikuo Kishimoto ◽  
Tadashi Asahina
Keyword(s):  
Thin Film ◽  
The Finite Element Method ◽  
Si Substrate ◽  
Detailed Structure ◽  
Micro Fabrication ◽  
Interfacial Toughness ◽  
Linear Elastic ◽  
Elastic Fracture ◽  
Cu Thin Film ◽  
Research Show

A new specimen is proposed to measure the interfacial toughness between the Al-0.5%Cu thin film and the Si substrate. The plain and general micro-fabrication processes are sufficient to fabricate the specimen. With the help of the finite element method and the concepts of the linear elastic fracture mechanics, the detailed structure for this specimen is modeled and evaluated. The results obtained from this research show that the proposed specimen provides efficient and convenient method to measure the interfacial toughness between the Al-Cu thin film and the Si substrate.

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