Issue 41

J.M. Vasco-Olmo et alii, Frattura ed Integrità Strutturale, 41 (2017) 166-174; DOI: 10.3221/IGF-ESIS.41.23

assumption D + F =0 must be made in order to give an appropriate asymptotic behaviour of the stress along the crack flank. Therefore, crack tip displacement fields are also defined from the same five coefficients.





HC z ln zF zF B z zHC z ln Fz

 



 

 

 

 













2 1

2 1

2 1

2 1

2 1





      Fz zF B 2 4 2 2



   2



iv uG 

2

4

4

(6)

  

 

 

 

2 1

2 1

2 1

 

zHC zD z ln zD zA

2

2

The CJP model provides three stress intensity factors to characterise the stress and displacement fields around the crack tip; an opening mode stress intensity factor K F , a retardation stress intensity factor K R , a shear stress intensity factor K S and also gives the T-stress. K F is defined from the applied remote load, traditionally characterized by K I , but is modified by force components derived from the stresses acting across the elastic-plastic boundary and which therefore influence the driving force for crack growth. Thus, K F is defined by evaluating the stress component σ y :       F B A r ln Fr r lim K y r F 8 3 2 2 2 2 1 0           (7) K R characterises forces applied in the plane of the crack and which provide a retarding effect on fatigue crack growth. Thus, K R is evaluated from σ x :     F r lim K x r R 2 3 2 2 0       (8) Besides the two previous SIFs, the CJP model proposes that a shear term arises from the requirement of compatibility at the elastic-plastic boundary of the plastically deformed crack wake. Therefore, this shear stress intensity factor ( K S ) characterises compatibility-induced shear stress along the plane of the crack at the interface between the plastic enclave and the surrounding elastic field. According to this, K S is defined from the shear stress component σ xy :     BA r lim K xy r S     2 2 0     (9) The T-stress is defined from its components in the x and y directions: T x = - C ; T y = - H .

E XPERIMENTAL WORK

A

compact tension (CT) specimen (dimensions shown in Fig. 1a) was manufactured from a 1 mm thick sheet of commercially pure titanium and subjected to constant amplitude fatigue loading at a R ratio of 0.6 ( P min = 450 N, P max = 750 N).

(a)

(b )

Figure 1 : (a) Dimensions (mm) of the CT specimen tested. (b) Experimental set-up used to measure DIC data during fatigue testing.

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