Analysis of the bi-material interface cracks based on configurational forces

2021 ◽  
pp. 1-23
Author(s):  
Ran Liu ◽  
Qun Li
Keyword(s):  
Interface Crack ◽  
Fracture Criterion ◽  
Crack Problem ◽  
Elastic Strain Energy ◽  
Crack Tip ◽  
Configurational Forces ◽  
Interface Fracture ◽  
Loading Conditions ◽  
Interface Cracks ◽  
Wide Range

Abstract In this paper, an innovative interface fracture criterion is proposed based on the concept of configurational forces in material space. In this criterion, the crack tip configurational forces as driving force is introduced to describe the interface crack evolution under mixed mode loading conditions. And it assumes that the interface crack propagates due to the competition of resultant of configurational forces with interface fracture toughness. The analytical expression of the configurational forces are obtained by differentiating the elastic strain energy density and conservative integral for interface cracks. And the relation of interface crack tip configurational forces with classical complex intensity factors are obtained through strict mathematical deduction. The interface crack tip configurational forces are evaluated for a classic interface crack problem covering a wide range of bi-material oscillation index. The configurational forces based interface fracture criterion is validated through series interface fracture experiments. The proposed criterion may provide a novel framework for analysis of interface fracture under complex loading conditions.

scholarly journals On stationary and moving interface cracks with frictionless contact in anisotropic bimaterials

1993 ◽  
Vol 443 (1919) ◽  
pp. 563-572
Keyword(s):  
Crack Problem ◽  
Stress Singularity ◽  
Crack Tip ◽  
Substantial Part ◽  
Open Crack ◽  
Interface Cracks ◽  
Complete Representation ◽  
Crack Tip Fields ◽  
Out Of Plane ◽  
Anisotropic Bimaterials

The asymptotic structure of near-tip fields around stationary and steadily growing interface cracks, with frictionless crack surface contact, and in anisotropic bimaterials, is analysed with the method of analytic continuation, and a complete representation of the asymptotic fields is obtained in terms of arbitrary entire functions. It is shown that when the symmetry, if any, and orientation of the anisotropic bimaterial is such that the in-plane and out-of-plane deformations can be separated from each other, the in-plane crack-tip fields will have a non-oscillatory, inverse-squared-root type stress singularity, with angular variations clearly resembling those for a classical mode II problem when the bimaterial is orthotropic. However, when the two types of deformations are not separable, it is found that an oscillatory singularity different than that of the counterpart open-crack problem may exist at the crack tip for the now coupled in-plane and out-of-plane deformation. In general, a substantial part of the non-singular higher-order terms of the crack-tip fields will have forms that are identical to those for the counterpart open-crack problem, which give rise to fully continuous displacement components and zero tractions along the crack surfaces as well as the material interface.

The r−1/2 (ln r) Singularities at Interface Cracks in Monoclinic and Isotropic Bimaterials due to Heat Flow

1993 ◽  
Vol 60 (2) ◽  
pp. 432-437 ◽  
Author(s):  
G. Yan ◽  
T. C. T. Ting
Keyword(s):  
Heat Flow ◽  
Interface Crack ◽  
Simple Form ◽  
Crack Tip ◽  
Higher Order ◽  
Stress Singularities ◽  
Interface Cracks ◽  
Existence Conditions

It is known that the stress singularities at an interface crack tip of bimaterials with the effects of heat flow may have the form r−1/2 (ln r). The existence conditions of the higher order singularitiy r−1/2 (ln r) are studied for monoclinic bimaterials whose plane of symmetry is at x3 = 0. It is shown that the higher order singularity does not exist if the bimaterial is mismatched. If the bimaterial is non-mismatched, the higher order singularity does not exist when a certain condition is satisfied. This condition is given explicitly for monoclinic bimaterials with the plane of symmetry of x3 = 0 and in a simple form for isotropic bimaterials.

The Mixed Mode I and II Interface Crack in Piezoelectromagneto–Elastic Anisotropic Bimaterials

2006 ◽  
Vol 74 (4) ◽  
pp. 614-627 ◽  
Author(s):  
R. Li ◽  
G. A. Kardomateas
Keyword(s):  
Magnetic Field ◽  
Energy Release Rate ◽  
Energy Release ◽  
Interface Crack ◽  
Release Rate ◽  
Plane Deformation ◽  
Crack Problem ◽  
Crack Tip ◽  
Electro Magnetic ◽  
Anisotropic Bimaterials

Taking the electric–magnetic field inside the interface crack into account, the interface crack problem of dissimilar piezoelectromagneto (PEMO)–elastic anisotropic bimaterials under in-plane deformation is investigated. The conditions to decouple the in-plane and anti-plane deformation is presented for PEMO–elastic biaterials with a symmetry plane. Using the extended Stroh’s dislocation theory of two-dimensional space and the analytic continuition principle of complex analysis, the interface crack problem is turned into a nonhomogeneous Hilbert equation in matrix notation. Four possible eigenvalues as well as four eigenvectors for the fundamental solution to the corresponding homogeneous Hilbert equation are found, so are four modes of singularities for the fields around the interface crack tip. These singularities are shown to have forms of r−(1∕2)±iϵ1 and r−(1∕2)±iϵ2, in which the bimaterial constants ϵ1 and ϵ2 are proven to be real numbers for practical dissimilar PEMO–elastic bimaterials. Compared with the solution for the interface crack of dissimilar elastic bimaterials without electro–magnetic properties, two new additional singularities are discovered for the interface crack in the PEMO–elastic bimaterial media. The electric–magnetic field inside the crack is solved by employing the “energy method,” which is based on finding the stationary point of the saddle surface of the energy release rate with respect to the electro–magnetic field inside the crack. Closed form expressions for the extended crack tip stress fields and crack open displacements are formulated, so are some other fracture characteristic parameters, such as the extended stress intensity factors and energy release rate (G) for dissimilar PEMO–elastic bimaterial solids. Finally, fundamental results and some conclusions are presented, which could have applications in the failure of piezoelectro/magneto–elastic devices.

Stress Intensity Factor of a Central Interface Crack in a Bonded Strip under Arbitrary Material Combination

2011 ◽  
Vol 462-463 ◽  
pp. 1146-1151
Author(s):  
Naoaki Noda ◽  
Yu Zhang ◽  
Xin Lan ◽  
Kentaro Takaishi
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Interface Crack ◽  
Crack Tip ◽  
Material Combination ◽  
Interface Cracks ◽  
Axial Tension ◽  
Crack Problems ◽  
Previously Treated

Although a lot of interface crack problems were previously treated, few solutions are available under arbitrary material combination. This paper deals with one central interface crack and numerical interface cracks in a bonded strip. Then, the effects of material combination on the stress intensity factors are discussed. A useful method to calculate the stress intensity factor of interface crack is presented with focusing on the stress at the crack tip calculated by the finite element method. For one central interface crack, it is found that the results of bonded strip under remote uni-axial tension are always depending on the Dunders’ parameters , and different from the well-known solution of the central interface crack under internal pressure that is only depending on . Besides, it is shown that the stress intensity factor of bonded strip can be estimated from the stress of crack tip in the bonded plate when there is no crack. It is also found that when , when , and when . For numerical interface cracks , values of and with arbitrary material combination expressed by , are obtained.

Intersection of Interface Crack Front with Free Edge

2014 ◽  
Vol 627 ◽  
pp. 225-228 ◽  
Author(s):  
Alex Møberg ◽  
Michal K. Budzik ◽  
Henrik M. Jensen
Keyword(s):  
Interface Crack ◽  
Crack Front ◽  
Fracture Criterion ◽  
Free Edge ◽  
Interface Fracture ◽  
Special Focus ◽  
Type Specimens ◽  
Elastic Mismatch ◽  
Beam Type ◽  
Elastic Layers

Delamination in layered materials is analyzed in a fracture mechanical framework. The work deals with quasi-static propagation of crack fronts along planar interfaces between different isotropic, elastic layers. Special focus is here on local effects at the sides of the layers which are assumed to be stress free. The interface crack front meets the free sides of the specimen at an angle which depends on the elastic mismatch in the system. Finite element calculations allowing the shape of the crack front to be arbitrary are carried out for double cantilever beam type specimens. An iterative procedure is formulated which adjusts the shape of the crack front so that an interface fracture criterion is satisfied locally along the front. Apart from the overall shape of the crack front, the angle of intersection with the free sides is in particular determined numerically by this procedure. Comparisons with analytical formulations and experimental results are performed.

scholarly journals Comparison of Modified Mohr–Coulomb Model and Bai–Wierzbicki Model for Constructing 3D Ductile Fracture Envelope of AA6063

2021 ◽  
Vol 34 (1) ◽  
Author(s):  
Jianye Gao ◽  
Tao He ◽  
Yuanming Huo ◽  
Miao Song ◽  
Tingting Yao ◽  
...  
Keyword(s):  
Ductile Fracture ◽  
Fracture Criterion ◽  
Fracture Strain ◽  
Stress Triaxiality ◽  
Ductile Fracture Criterion ◽  
Forming Process ◽  
Tension Tests ◽  
Wide Range ◽  
Round Bar ◽  
Fracture Envelope

AbstractDuctile fracture of metal often occurs in the plastic forming process of parts. The establishment of ductile fracture criterion can effectively guide the selection of process parameters and avoid ductile fracture of parts during machining. The 3D ductile fracture envelope of AA6063-T6 was developed to predict and prevent its fracture. Smooth round bar tension tests were performed to characterize the flow stress, and a series of experiments were conducted to characterize the ductile fracture firstly, such as notched round bar tension tests, compression tests and torsion tests. These tests cover a wide range of stress triaxiality (ST) and Lode parameter (LP) to calibrate the ductile fracture criterion. Plasticity modeling was performed, and the predicted results were compared with corresponding experimental data to verify the plasticity model after these experiments. Then the relationship between ductile fracture strain and ST with LP was constructed using the modified Mohr–Coulomb (MMC) model and Bai-Wierzbicki (BW) model to develop the 3D ductile fracture envelope. Finally, two ductile damage models were proposed based on the 3D fracture envelope of AA6063. Through the comparison of the two models, it was found that BW model had better fitting effect, and the sum of squares of residual error of BW model was 0.9901. The two models had relatively large errors in predicting the fracture strain of SRB tensile test and torsion test, but both of the predicting error of both two models were within the acceptable range of 15%. In the process of finite element simulation, the evolution process of ductile fracture can be well simulated by the two models. However, BW model can predict the location of fracture more accurately than MMC model.

Solution for a Semi-Permeable Interface Crack in Elastic Dielectric/Piezoelectric Bimaterials

2008 ◽  
Vol 75 (1) ◽  
Author(s):  
Q. Li ◽  
Y. H. Chen
Keyword(s):  
Electric Field ◽  
Mechanical Loading ◽  
Interface Crack ◽  
Applied Electric Field ◽  
Crack Tip ◽  
Crack Model ◽  
Permeable Crack ◽  
Impermeable Crack ◽  
Silicon Oil ◽  
Elastic Dielectric

A semi-permeable interface crack in infinite elastic dielectric/piezoelectric bimaterials under combined electric and mechanical loading is studied by using the Stroh complex variable theory. Attention is focused on the influence induced from the permittivity of the medium inside the crack gap on the near-tip singularity and on the energy release rate (ERR). Thirty five kinds of such bimaterials are considered, which are constructed by five kinds of elastic dielectrics and seven kinds of piezoelectrics, respectively. Numerical results for the interface crack tip singularities are calculated. We demonstrate that, whatever the dielectric phase is much softer or much harder than the piezoelectric phase, the structure of the singular field near the semi-permeable interface crack tip in such bimaterials always consists of the singularity r−1∕2 and a pair of oscillatory singularities r−1∕2±iε. Calculated values of the oscillatory index ε for the 35 kinds of bimaterials are presented in tables, which are always within the range between 0.046 and 0.088. Energy analyses for five kinds of such bimaterials constructed by PZT-4 and the five kinds of elastic dielectrics are studied in more detail under four different cases: (i) the crack is electrically conducting, (ii) the crack gap is filled with air/vacuum, (iii) the crack gap is filled with silicon oil, and (iv) the crack is electrically impermeable. Detailed comparisons on the variable tendencies of the crack tip ERR against the applied electric field are given under some practical electromechanical loading levels. We conclude that the different values of the permittivity have no influence on the crack tip singularity but have significant influences on the crack tip ERR. We also conclude that the previous investigations under the impermeable crack model are incorrect since the results of the ERR for the impermeable crack show significant discrepancies from those for the semi-permeable crack, whereas the previous investigations under the conducting crack model may be accepted in a tolerant way since the results of the ERR show very small discrepancies from those for the semi-permeable crack, especially when the crack gap is filled with silicon oil. In all cases under consideration the curves of the ERR for silicon oil are more likely tending to those for the conducting crack rather than to those for air or vacuum. Finally, we conclude that the variable tendencies of the ERR against the applied electric field have an interesting load-dependent feature when the applied mechanical loading increases. This feature is due to the nonlinear relation between the normal electric displacement component and the applied electromechanical loadings from a quadratic equation.

Stress Field of Semi-Infinite Interface Crack Tip of Double Dissimilar Orthotropic Composite Materials

2010 ◽  
Vol 97-101 ◽  
pp. 1223-1226
Author(s):  
Jun Lin Li ◽  
Shao Qin Zhang
Keyword(s):  
Composite Material ◽  
Composite Materials ◽  
Interface Crack ◽  
Interfacial Crack ◽  
Crack Tip ◽  
Stress Fields ◽  
Displacement Fields ◽  
Orthotropic Composite ◽  
Stress Functions ◽  
Secular Equations

The problem of orthotropic composite materials semi-infinite interfacial crack was studied, by constructing new stress functions and employing the method of composite material complex. In the case that the secular equations’ discriminates the and theoretical solutions to the stress fields and the displacement fields near semi-infinite interface crack tip without oscillation and inter-embedding between the interfaces of the crack are obtained, a comparison with finite element example was done to verify the correction of theoretical solution.

A Review of K-Solutions for Through-Thickness Flaws in Cylinders and Spheres

2007 ◽  
Author(s):  
Ali Mirzaee Sisan ◽  
Isabel Hadley ◽  
Sarah E. Smith ◽  
Mike Smith
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Loading Conditions ◽  
Wide Range ◽  
Cylinders And Spheres

This paper reviews different stress intensity factor solutions for a wide range of configurations and loading conditions for a cylinder with axial and circumferential through thickness cracks and a sphere with through thickness meridional (equatorial) cracks. The most appropriate solutions to use are identified.

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