Determination of stress concentrator opening displacement

Panasyuk, V. V.; Ivanitska, G.S.; Ostash, О. P.

doi:10.1016/0013-7944(95)00108-5

Cited by 5 publications

(9 citation statements)

References 5 publications

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“…2) are nonlinear. Indeed, calculations by the rule of similarity of triangles, according to which the opening displacement of the crack tip is calculated by the opening measured at the end of the specimen [6], are not true for the entire range of variable p. This fact is also confirmed by the analytic data given in [4]. Nevertheless, in a small vicinity of the tip of notches, these dependences are linear and, for all values of p, intersect the OX-axis at a point (at a certain distance rp) behind the tip of the notch (see Fig.…”

Section: Low-plastic Materialsmentioning

confidence: 64%

“…Among them, for example, the COD and CTOD [6,7], COA and CTOA [8], ASef f [9], and ~5 [I0] approaches as well as the method of marks [11] should be mentioned. Note that, contrary to the previously known methods regulated by BS (British Standards) [6], the estimation of the value of 8 immediately in the vicinity of the tip of a crack [10] or near the tip of a notch [4,5] is considered now as the main problem.In this work, we present the results of investigation of the possibility of use of strain criteria in determination of the period N i prior to the nucleation of fatigue macrocracks near stress concentrators in certain steels and aluminum alloys. In our investigations, we employ the concept [2] that the main parameters of the process of nucleation of a macrocrack are the range Ae* of local elastoplastic strains near the tip of a notch and the characteristic size a t* of the prefracture zone.…”

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confidence: 98%

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Unified model of nucleation and growth of fatigue macrocracks. Part 2. Application of deformational parameters of the fracture mechanics of materials in the stage of crack initiation

Ostash¹,

Panasyuk²,

Kostyk³

1998

Mater Sci

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We propose a new approach to the experimental estimation of local strains at the tip of a concentrator. The approach is based on the measurement of displacement of certain points in the vicinity of the tip of a notch, which is further associated with the effective radius of the notch. Various concentrators in structures are simulated within a wide range of variation in radii of notches (p = 0.1-6.5 mm ) and in the geometry of specimens. We establish the main dependences between the value of the range of local strains Ae* and the period N i prior to the nucleation of a fatigue macrocrack. Thus, by using the experimental quantity Ae*, we can estimate the period N i prior to the nucleation of a fatigue crack of length a i = ae for structural elements of a complicated geometry.As is known, the problem of fatigue fracture of materials is an actual problem of modern materials science and fracture mechanics of materials [ 1,2]. In solution of this problem, investigation of the nucleation of macrocracks near stress concentrators in structural elements plays an important role. For this purpose, the force (stress), strain, and energetic parameters of the stress-strain state of the material are mainly used. The force approach to solution of the problem was earlier considered in [2]. Owing to the difficulty of calculations of stresses (force parameters) in the vicinity of various concentrators in structural elements during their service, especially with regard for elastoplastic strains of material and the action of the environment (working medium), it is necessary to search for the most simple approaches to solution of the problem. To a certain extent, this can be realized by using the strain parameters, because strains can not only be calculated but measured directly on members as well.Local strains can be determined, for example, in terms of relative displacements of the lips of a notch [1-3] or a crack [6][7][8][9][10][11]. In particular, this was corroborated by numerous attempts (during the last 5-10 years) to use strain criteria on the basis of the characteristics of the relative displacement 8 in analysis of the kinetics of cracks in a deformable body. Among them, for example, the COD and CTOD [6,7], COA and CTOA [8], ASef f [9], and ~5 [I0] approaches as well as the method of marks [11] should be mentioned. Note that, contrary to the previously known methods regulated by BS (British Standards) [6], the estimation of the value of 8 immediately in the vicinity of the tip of a crack [10] or near the tip of a notch [4,5] is considered now as the main problem.In this work, we present the results of investigation of the possibility of use of strain criteria in determination of the period N i prior to the nucleation of fatigue macrocracks near stress concentrators in certain steels and aluminum alloys. In our investigations, we employ the concept [2] that the main parameters of the process of nucleation of a macrocrack are the range Ae* of local elastoplastic strains near the tip of a notch and the characteristic size a t* ...

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Section: Low-plastic Materialsmentioning

confidence: 64%

mentioning

confidence: 98%

Unified model of nucleation and growth of fatigue macrocracks. Part 2. Application of deformational parameters of the fracture mechanics of materials in the stage of crack initiation

Ostash¹,

Panasyuk²,

Kostyk³

1998

Mater Sci

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“…We determine the stress intensity factors at the tips x 2 = 12 and x 4 =/4 of the cuts L 2 and L 4 by the formulas [14] Xz--+l 2 12 gZ(X2) and KII(/4) = x41im-+~4 14 g4(x4).…”

Section: G ~ G2(t2)dt2mentioning

confidence: 99%

“…However, in many cases (in particular, in disks with central cracks [6]), under loads of certain types, we observe the appearance of new bands inclined to the line of continuation of the crack. Neglecting these inclined bands, we get underestimated values of the displacement ~ [12].In the present work, within the framework of the model of plasticity bands, we solve the problem of elastoplastic equilibrium of a disk with central crack and study the influence of inclined plasticity bands on the crack tip opening displacement. …”

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confidence: 99%

Tension of an elastoplastic disk. Part 1. Central crack

Panasyuk¹,

Savruk²,

Ivanyts'ka³

et al. 1999

Mater Sci

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539.375 Within the framework of the model of plasticity bands, we consider an elastoplastic problem of fracture mechanics of the development of plasticity bands near the tips of a central crack in a disk. We assume that, in the plane stressed state, plastic strains in the vicinity of the crack tip are localized along three plasticity bands (L I , L 2 , and L~ ) one of which is located on the continuation of the crack and the other two make nonzero angles with the direction of the crack and that, under the conditions of plane deformation, plastic strains are localized along two plasticity bands (L I and ~ ). The band (~) is modeled by a line of discontinuity of normal and tangential displacements and the bands (L l and L 2) are modeled by lines of discontinuity of tangential displacements. The lengths and orientations of these lines are determined in the process of numerical solution of the problem by the method of singular integral equations. The values of the crack tip opening displacement are also determined.Disk specimens with notches or cracks are used in the investigation of the processes of initiation and development of cracks under static and cyclic loading [1][2][3][4]. The level of local strains near a concentrator characterized by the jump of normal displacements (opening displacement) at its tip 6 can be regarded as a parameter that controls these processes in elastoplastic materials. To find this parameter, it is necessary to solve the problem of determination of the strain-stress state of the disk taking into account elastoplastic strains near the tip of the concentrator. For this purpose, we use the model of plasticity bands (see, e.g., [5-1 1]) according to which the plasticity zone is localized along narrow bands lying on the continuations of the crack. As follows from the experimental data presented in [5][6][7], this model reflects the actual process of deformation in the first stage of the development of plastic strains in thin plates. However, in many cases (in particular, in disks with central cracks [6]), under loads of certain types, we observe the appearance of new bands inclined to the line of continuation of the crack. Neglecting these inclined bands, we get underestimated values of the displacement ~ [12].In the present work, within the framework of the model of plasticity bands, we solve the problem of elastoplastic equilibrium of a disk with central crack and study the influence of inclined plasticity bands on the crack tip opening displacement. Plane Stressed StateA thin disk of radius R containing a central crack L 1 of length 2/1 is related to a Cartesian coordinates xOy. The disk is subjected to tension by two concentrated forces F applied at points Zo = + ih (Fig. 1). The material of the disk is perfectly elastoplastic.In the disk subjected to tension, near the crack tips, we first observe the appearance of plastic bands directed along the continuation of the crack. Further, as the load increases, we observe the appearance of two additional bands at each tip making nonzero an...

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“…Local strain due to the notch 3–5 or crack 6–11 can be estimated by the opening displacement, δ . In particular, numerous applications have used the opening displacement, based on strain parameters, in crack growth analyses during the last 5–10 years.…”

Section: Introductionmentioning

confidence: 99%

Assessment of the period to fatigue macrocrack initiation near stress concentrators by means of strain parameters

Ostash

Panasyuk

Kostyk

1999

Fatigue Fract Eng Mat Struct

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A new approach to the experimental assessment of the local strain at a stress concentrator has been presented. It is based on a procedure of notch opening displacement measurements at certain points in the vicinity of a notch related to the effective notch radius ρeff = ρ + d *, where ρ is the notch radius and d * is a material constant. Different stress concentrators in structural elements were modelled for a wide variation of notch radii (ρ = 0.1–6.5 mm) and different geometries of specimens. Hence, a basic relationship, which directly relates the local strain range Δε* to the period of fatigue macrocrack initiation Ni has been established. Thus, by applying the value of Δε* , assessed from a direct measurement at the notch root, it is possible to determine the period Ni to initiate a fatigue macrocrack of length ai = d * for some structural components of complicated geometry.

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Determination of stress concentrator opening displacement

Cited by 5 publications

References 5 publications

Unified model of nucleation and growth of fatigue macrocracks. Part 2. Application of deformational parameters of the fracture mechanics of materials in the stage of crack initiation

Unified model of nucleation and growth of fatigue macrocracks. Part 2. Application of deformational parameters of the fracture mechanics of materials in the stage of crack initiation

Tension of an elastoplastic disk. Part 1. Central crack

Assessment of the period to fatigue macrocrack initiation near stress concentrators by means of strain parameters

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