Calculation of J 1 and J 2 using the L and M integrals

Kienzler, Reinhold; Kordisch, H.

doi:10.1007/bf00018343

Cited by 16 publications

(9 citation statements)

References 21 publications

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“…Peculiar variation of this configurational force with the distance between the inclusion and the free surface is noted and discussed. The determination of physical quantities, such as the dislocation interaction force or the stress-intensity factor in various dislocation and fracture mechanics problems, without solving the corresponding boundary value problems, was earlier considered by Eshelby [1975], Freund [1978], Rice [1985], Kienzler and Kordisch [1990], and Lubarda and Markenscoff [2007], among others. More recently, Lubarda [2015] employed the antiplane-strain version of the Kienzler-Zhuping formula, first recognized by Lin et al [1990], to determine the configurational force between a circular void and inclusion characterized by uniform eigenshear.…”

Section: Introductionmentioning

confidence: 99%

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Lubarda

2015

J. Mech. Mater. Struct.

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The interaction force between a circular inclusion characterized by uniform eigenstrain and a nearby circular void is determined by evaluating the J-integral around the void. The Kienzler-Zhuping formula was used to determine the hoop stress along the boundary of the void in terms of the infinite-medium solution to the inclusion problem. Specific results are given for the inclusion with dilatational eigenstrain. The M-integrals around the void and inclusion are then evaluated, the former being proportional to the energy release rates associated with a self-similar expansion of the void. The energy rate associated with an isotropic expansion of the inclusion differs from the M-integral around the inclusion. The relationship between the two is derived. It is shown that the greater the distance from the void, the greater the energy associated with the presence of the inclusion and the greater the energy rate associated with its growth, which suggests that the presence of nearby free surfaces facilitates the eigenstrain transformations. The attraction exerted on a circular inclusion with a uniform shear eigenstrain by the free surface of a halfspace is also evaluated. Peculiar variation of this configurational force with the distance between the inclusion and the free surface is noted and discussed.

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Section: Introductionmentioning

confidence: 99%

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Lubarda

2015

J. Mech. Mater. Struct.

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“…L and M depend on the choice of the point of reference. Choosing for L the origin of the coordinate system and for M the center of the hole, the path-independent integrals have been evaluated (Kienzler and Herrmann 2000;Kienzler and Kordisch 1990) and are given as…”

Section: Interaction Of An Edge Dislocation With a Circular Holementioning

confidence: 99%

Reciprocity in fracture and defect mechanics

Kienzler

2007

Int J Fract

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“…It is worth mentioning that this relation holds for cases where e < 1. In fact, this line of reasoning was used before by Kienzler and Zhuping [9], Kienzler and Kordisch [3], and Kienzler [1] to assess the interaction between a circular hole and an edge dislocation through J-integral evaluation. As mentioned by Rice [8] the corresponding J-integral contribution is given by: where ao~ denotes the hoop stress with respect to the local peripheral coordinate system as indicated in Fig.…”

Section: Epicycloidal Cusp-like Cracksmentioning

confidence: 99%

Applications of the concept of J-integrals for calculation of generalized forces

Müller

Kemmer

1998

Acta Mechanica

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The J-integral technique is used to assess the risk of defects in a particular structure by explicit computation of the arising generalized forces. Three different situations are considered: stress concentrators in cycloidal specimens, the interaction of a dislocation with a circular inclusion, and the interaction between two dislocations. Special emphasis is given to an effective but analytical calculation of the corresponding path integrals. IntroductionEver since the pioneering work of Eshelby and Rice the J-integral has been known to be an effective way of assessment of the risk of defects in a structure. In fact, it can be used to quantify various kinds of "defects" in a very broad sense of the word. The term "defect" can refer to the singular stress-strain field developing around the tip of a crack which illustrates the crucial importance of the concept of J-integrals in fracture mechanics. The defect can also be a stress concentrator like a notch or, on a more elementary scale, apply to imperfections in crystals, such as dislocations (e.g., Kienzler [1]).The purpose of this paper is, first, to illustrate the possibility to obtain closed-form solutions for the J-integral in the aforementioned situations by suitable choice of the integration path. Second, the attention is drawn to the potential of epicycloidal specimens for use in fracture mechanics. The J-integral will explicitly be evaluated for epicycloids of order 1 and 2 which are subjected to thermal loading by a central hot spot. Energy release rates will be computed for cusp-like notches and then be used to predict the stress intensity factors of cusp-like cracks in such specimens (Section 3.1). Third, for the case of dislocation problems, it will be shown that the evaluation of the path integral can be extremely facilitated if a certain limit procedure is applied (Section 3.2 and 3.3). Theoretical backgroundConsider a closed surface, ~ V, in three-dimensional space. In the static case under absence of body forces, for small deformations, and within the framework of deformation theory the J-integral is defined as follows (e.g., Rice [17], Buggisch, Gross and Kriiger [2], Kienzler and Kordisch [3], or W.H. Miiller and G. Kemmer Kienzler [1]):

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Calculation of J 1 and J 2 using the L and M integrals

Cited by 16 publications

References 21 publications

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Reciprocity in fracture and defect mechanics

Applications of the concept of J-integrals for calculation of generalized forces

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