A complete field method for the photoelastic determination of KI and KII in general mixed-mode fracture

Picón, Rafael; Parı́s, F.; Cañas, J. A.; Marin, Juan L

doi:10.1016/0013-7944(94)00210-9

Cited by 12 publications

(9 citation statements)

References 13 publications

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“…The technique has been found to be robust for predominantly mode I1 cracks, as well as mode I and other mixed mode cases [9] and in the vicinity of other singularities and boundaries [ 111. A similar approach has been adopted more recently by Picon et al [12].…”

Section: Introductionmentioning

confidence: 99%

On Determining Stress Intensity Factors for Mixed Mode Cracks From Thermoelastic Data

Tomlinson

Nurse

Patterson

1997

Fatigue Fract Eng Mat Struct

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An alternative methodology is presented for determining stress intensity factors for cracks subject to mixed-mode displacements. The methodology involves thermoelastic data generated from a SPATE (Stress Pattern Analysis by Thermal Emission) system and has been adapted from one used successfully in photoelasticity. The thermoelastic data is collected throughout the elastic stress field dominated by the crack tip singularity. The stress field is described using a Fourier series within Muskhelishvili's approach. This method allows different applied stress fields to be described which may include transient or non-uniform stress fields. The results obtained using the new methodology are at least as good as those obtained previously for pure mode I cases, and generally better for mixed mode displacement conditions. NOMENCLATURE a = crack length or crack half length A = SPATE calibration factor AN, BN, h, b. = series coefficients of the stress field equations cg = specific heat for constant deformation E = Young's modulus m = shape of the mapped circle M = mass r, 0 = polar co-ordinates in mapping plane R = arbitrary length parameter S = SPATE signal T = temperature V = volume W = panel width x, y = rectangular co-ordinates in the physical plane z = x + iy = complex variable in the physical plane a = thermal expansion coefficient [ = r(cos 0 + i sin 0) = complex variable in mapping plane p = crack tip radius ol, n2, a, = principal stress 5 = shear stress v = Poisson's ratio @, !P= analytical stress functions of a complex variable 4 = cos 0 + i sin 0 = complex variable in mapping plane defining unit circle w = mapping function Z = conjugate of complex variable (2) Complex notation Superscript (') = denotes differentiation 217 218 R. A. TOMLINSON et al.

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Section: Introductionmentioning

confidence: 99%

On Determining Stress Intensity Factors for Mixed Mode Cracks From Thermoelastic Data

Tomlinson

Nurse

Patterson

1997

Fatigue Fract Eng Mat Struct

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“…By contrast, because photoelasticity provides only the elastic strain fields in the birefringent coating, it is mainly used to determine experimentally stress intensity factors for complex loading modes in components where the fields are predominantly linear elastic [24][25][26][27]. Because constraint effects that arise in elastic-plastic materials are then weak, such experimental data agree reasonably well with theoretical plane-stress solutions.…”

Section: Introductionmentioning

confidence: 76%

Investigation of crack-tip plasticity in high volume fraction particulate metal matrix composites

Miserez

Rossoll

Mortensen

2004

Engineering Fracture Mechanics

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Crack-tip strain fields in high volume fraction ceramic particle reinforced metal matrix composites are assessed using photoelastic measurements. It is shown that the size of the significant crack-tip plastic zones that form in these materials depends on the type and diameter of the reinforcement and on the matrix material. This plastic zone size correlates well with the macroscopic toughness values assessed through J -integral testing. The composites are thus ''metallic'' in the sense that their toughness is mostly composed of plastic energy dissipation around the crack tip. Plastic deformation also induces marked constraint effects that influence the shape of the surface strain fields. It is shown that finite element analysis must be three-dimensional to describe these strain fields, as two-dimensional plane-stress analysis fails to reproduce the experimental data.

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“…Subsequently, Sanford 19 extended the MPODM by allowing the position of the crack tip to be unknown in the solution. In recent years, an additional degree of sophistication has been introduced 20,21 by using Muskhelishvili's approach to describe the stress field around the crack tip. Westergaard's equations assume that the crack is propagating through a uniform stress field.…”

Section: Outline Of the Techniquesmentioning

confidence: 99%

Optical analysis of crack tip stress fields: a comparative study

Patterson

Olden

2004

Fatigue Fract Eng Mat Struct

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A B S T R A C T Four optical techniques for evaluating stress intensity factors in opaque specimens are described in outline, and compared for both an artificial crack and a fatigue crack. The results are compared to a standard solution for the geometry considered. All the techniques gave acceptable results over a range of stress levels and crack lengths. The methods of caustics and strain gauges were less good, whilst photoelasticity gave consistent results over a wide range of stress levels. Comments on the ease of application and the resource implications are also made in order to assist practitioners.= diameter of caustic (as measured on screen) E = modulus of elasticity f σ = material stress fringe constant F 0 , F 1 , G 0 = unknown coefficients in strain gauge solution g i = error function (photoelastic MPODM) h i = error function (thermoelastic MPODM) j = √ −1 = complex number k = (1 − υ)/(1 + υ) K I , K II = mode I and II stress intensity factors, respectively K AP = normalized apparent stress intensity factor (K AP = τ max √ 8πr) l = length of light path through photoelastic specimen L = length of strain gauge N (N m ) = photoelastic fringe order (value at (r m , θ m )) N x = moiré fringe order at (r, π/ 2) p = pitch of moiré reference grating P = applied load q = focal length of lens in caustic apparatus r = polar coordinate with origin at crack tip r c = distance from crack tip to geometric centre of strain gauge r m = distance from crack tip to photoelastic fringe apogee s(σ 0 i,j ) = a set of constants S = thermoelastic signal t = specimen thickness u = distance from specimen to lens in caustic apparatusCorrespondence: E. A. Patterson.

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A complete field method for the photoelastic determination of KI and KII in general mixed-mode fracture

Cited by 12 publications

References 13 publications

On Determining Stress Intensity Factors for Mixed Mode Cracks From Thermoelastic Data

On Determining Stress Intensity Factors for Mixed Mode Cracks From Thermoelastic Data

Investigation of crack-tip plasticity in high volume fraction particulate metal matrix composites

Optical analysis of crack tip stress fields: a comparative study

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