PSI - Issue 18

A.P. Zakharov et al. / Procedia Structural Integrity 18 (2019) 749–756 A.P. Zakharov / Structural Integrity Procedia 00 (2019) 000 – 000

750

2

1. Introduction According to Hu tchinson’s (1968) analytical solution, the near-tip field at a stationary Mode I crack for an elastic – plastic power hardening material is governed by the plastic SIF which plays a role analogous to that of elastic SIF and it is directly related to J -integral by a simple equation for small-scale yielding conditions. Shih (1974) extended the HRR solution for the small-scale yielding mixed-mode fracture and showed that an important feature of such analysis is the formulation of the additional parameter governing singular stress fields for an elastic – plastic material. Hilton and Hutchinson (1971), Hilton and Sih (1973) and Hilton (1973) investigated the behaviour of the plastic stress or strain intensity factor, for both the small- and large-scale yielding ranges. Shlyannikov and Tumanov (2014) proposed a new method for solving problems for the complete range of mixed mode loadings between Mode I and Mode II and obtained the reference fields for plane mixed-mode problems governing the asymptotic behaviour of the stresses and strains at the crack tip in elastic – plastic material. In the literature there is practically no systematic computational data on the coupled effect of the finite radius of curvature and biaxial loading on the crack tip stress fields and fracture resistance parameters. In this paper the plastic SIF is used to study the coupling effects of loading biaxiality, material properties and crack tip configuration in both the small- and large-scale yielding ranges. A finite element (FE) analysis was performed for a cracked Mode I plate subjected to biaxial tension/compression loading. The governing parameter of the elastic – plastic crack-tip stress field I n -integral at the crack tip, J -integral, and the plastic SIF, were calculated as functions of crack tip configuration, loading biaxiality and applied stress levels. Special emphasis is put on the behavior of J -integral and the plastic SIF for specified test specimen geometries under mixed mode loading. 2. Plastic stress intensity factor for small- and large-scale yielding For an infinite plate with a centred line crack subjected to mixed-mode loading, the plastic SIF K P and the J integral are related by Shih’s (1974) relation for small-scale conditions, which is represented as:           2 2 2 1 2 2 0 1 2 1 2 1 1 2 1 1 , , 4 4 n x y n P x y J J J I K J K K J K K E E E                   (1) where the components of the J- integral on the embedded Cartesian coordinates are defined in terms of elastic stress intensity factors K 1 and K 2 . Plastic SIF for mixed mode cracked bodies under small-scale yielding can be written as:

1



    

 



n

1



2





2

   1 1 4   

2 K K K K   2 4

I w   

1

2

1 2

K

 

(2)

P

2

0 

 

n

Elastic SIF for finite size cracked specimen under mixed mode loading conditions can be expressed in the following form:

a

a

  

 

  

  









K

a F 

Y

, T K 

a F 

Y

T

,  

, , 

,  

, , 









 

 

(3)

n

K

n

K

1

1

1

2

2

2

w

w

where a is crack length,  is crack angle,  n is nominal applied stress,  0 is yield stress,  is load biaxiality ratio, w is specimen width,  is the Poisson’s ratio, T is nonsingular stress, F Ki (  ,  ) are loading biaxiality and mode mixity factors, Y i (a/w,  ,T) are geometry dependent stress intensity correction factors.