The yield-point loads of singly-notched pin-loaded tensile strips

Ewing, D.J.F.; Richards, C.E.

doi:10.1016/0022-5096(74)90011-8

Cited by 77 publications

(34 citation statements)

References 11 publications

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“…To do this, the solutions of SIF and COD for the double edge cracks in plates of width h are found by solving a system of Cauchy-type singular integral equations. For the cases of tension and bending, the numerical results of plastic zone sizes and crack opening displacements from this improved D-M model are compared with those by Chell which take no account of the yielding at the back side [3] and with the experimental results [4]. From this improved D-M model, the envelopes for the beginning of backside yielding and ligament yielding are also obtained.…”

Section: Introductionmentioning

confidence: 99%

The improved D-M model solutions for single edge cracked plates by considering the yielding at the back side

Yinchu

Guo

1990

Int J Fract

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The method of calculating the stress intensity factor (SIF) and the crack opening displacement (COD) for double edge cracks in plates under arbitrary loadings that results in solving a system of Cauchy-type singular integral equations is presented. The improved D-M model is then constructed for edge cracked plates by considering the yielding at the back side. For the cases of tension and bending, the plastic zone sizes and the crack opening displacements are calculated from the improved model solution, and the envelopes for the beginning of backside yielding and ligament yielding are obtained. The numerical results are compared with known solutions which take no account of the yielding at the back side and with experimental results.

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Section: Introductionmentioning

confidence: 99%

The improved D-M model solutions for single edge cracked plates by considering the yielding at the back side

Yinchu

Guo

1990

Int J Fract

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“…where, b a x  and  is equal to 3 2 for von Mises yielding criterion and 1 for Tresca yielding criterion (Ewing & Richards, 1974). .…”

Section: Single-edge Tension Specimen (Se(t))mentioning

confidence: 99%

Limit analysis of cracked structure by combination of extended finite element method with linear matching method

Ri¹,

Hong²

2018

10.5267/j.esm

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Linear matching method (LMM) is one of the effective numerical methods for the limit and shakedown analysis, which computes the converging upper series by solving iteratively linear elastic analysis with Young's modulus varying in space. LMM, which is capable of implementing by using the commercial finite element packages such as ABAQUS and ANSYS has been widely used in the practical applications including fatigue, creep and composite analysis. Nevertheless, LMM could not ensure numerical accuracy for discontinuous problems such as crack analysis since it computes the mechanical quantities including stress, strain and displacement on the base of conventional finite element method, likewise other numerical methods for the limit and shakedown analysis. Meanwhile, extended finite element method (XFEM), recently proposed, is an attractive numerical method for the analysis of discontinuous problems which enriches finite element approximate space by some special functions. In this paper, authors proposed a very straightforward method for the limit analysis by the combination of XFEM with LMM. Numerical validation is done for two types of typical fracture specimens. Numerical examples show that the limit analysis by combining XFEM with LMM gives more accurate result compared with the one by combining of conventional finite element method with LMM. Furthermore, we demonstrated that the choice of enrichment region plays an important role in the improvement of numerical accuracy of our proposed method.

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“…(a) Three-point bend specimen: The silp-line solution for single-edge cracked specimen subjected to combined tension and bending obtained by Ewing and Richards [7] gives the s~.rne estimate as (5) for the compact tension specimen (a/W > 0.09). Table 1.…”

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confidence: 99%

Q solutions for compact tension and single-edge cracked tension specimens

Mai

Cotterell

1995

Int J Fract

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The J-Q two-parameter fracture theory proposed recently by O'Dowd and Shih [1][2][3] has shown that the stress fields in the forward sector ahead a crack tip under very general conditions of loading in finite bodies can be described by two parameters J and Q. The J-integral sets the scale of deformation at the crack tip (i.e. the CTOD) while the hydrostatic stress parameter, Q, quantifies the level of stress triaxiality ahead of the crack tip. The J-Q theory has been successfully applied to brittle cleavage fracture, ductile fracture and brittle-ductile fracture transition.O'Dowd and Shih [3] gave Q solutions for centre-cracked tension, double-edge cracked tension and three-point bend specimens with various crack lengths. Their solutions are based on the small scale yielding solution as the reference stress. In this report Q solutions for ASTM standard compact tension (C(T)) and singleedge cracked tension (SE(T)) specimens are presented and the dependence of the Q-parameter on the material properties is studied. We use the HRR stress as the reference and the definition of Q is [3] Q = ao0--(O'oo)HRR at 0 = 0 , r = 2 J / a o (1) (70 where ao is the yield stress of the material and aoo is the hoop stress and (~rOO)HRR is the HRR stress. Q values for these two geometries have been obtained by plane strain finite element analyses based on small strain deformation plasticity by use of ABAQUS Version 4-9 (HIBBITT, KARLSSON & SORENSEN, INC.). Eight-noded biquadratic displacement, linear pressure elements with reduced intergration are employed. Because of symmetry only one half of the specimen is analysed. 36 wedge-shaped collapsed eight-noded isoparametric elements are used to surround the upper half Int Journ of Fracture 68 R98of the crack tip. 73 nodes sharing initially the same location at the crack tip are allowed to displace independently. A typical mesh has about 1000 elements. The materials modelled obey the Ramberg-Osgood relationQ values for C(T) specimen with crack length-width ratio a / W = 0.3, 0.5, 0.6 and 0.7 are given in Fig.1. The modelled material is material A given in Table 1 but with various hardening exponent n = 3, 5, 10 and 20. In the figure, J is normalised by the crack length a for a/W = 0.3 and by the remaining ligament b = (W -a) for other crack lengths. For these crack lengths high stress triaxiality is maintained at lower deformation level of J/(aao) or J/(bao) less than about 0.01. At the higher deformation level, the global bending stress field causes a rapid decrease of the stress triaxiality. These results are similar to that obtained by O'Dowd and Shih [3] for three-point bend specimen. However, at the medium deformation level Q value decreases with increasing crack length a/W. This behaviour is different to other geometries and may be caused by the global bending stress having a stronger effect on large crack lengths. Since the HRR-stress is used as the reference stress, a significant effect of strain hardening on Q value is observed in that Q increases with increasing n as shown in F...

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The yield-point loads of singly-notched pin-loaded tensile strips

Cited by 77 publications

References 11 publications

The improved D-M model solutions for single edge cracked plates by considering the yielding at the back side

The improved D-M model solutions for single edge cracked plates by considering the yielding at the back side

Limit analysis of cracked structure by combination of extended finite element method with linear matching method

Q solutions for compact tension and single-edge cracked tension specimens

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