Crack Paths 2012

Table 1. Stress components and SIF functions on the crack flanks

stress components

center cracked plate

compact tension-shear

specimen

Kr 2

(

)

( ) α η 2 s1i n 1 −

=⎟ −

σσ

2

T

σ

2 π

+

2

xyy xx =

2

( )

ra2 cos1

σσ

Y wa T 2 2 =⎟ −

ar

Y wa T

α

⎜ ⎝ ⎛

⎞

⎜ ⎝ ⎛

⎞

xx

xx

π+ = θ

0 σ − = =

⎠

⎠

0

2 Kr 2

xy

(

)

( ) α η 2 s1 i n 1 −

σ σ =⎟ −

2

= =

+

T

σ

2 π

2

yy xx

a r T

(

)

Y wa

α

Y wa

σ σ xx =⎟ − ⎠ ⎞

2 T

ra2 cos1

⎜ ⎝ ⎛

⎞

⎜ ⎝ ⎛

xx

π− = θ

2

=

0

σ

⎠

0

σ

approximate procedure has been independently proposed by authors [5,6]. Essentially,

the procedure involves replacing the bent crack with a straight-line

crack

approximation. The present work explores direct use of F E Manalysis for calculating T- stress on the base of crack flank nodal displa ements [7]. Using th technique, first of

all the T-stress distributions in various specimen geometries was determined from

numerical calculations. Then on this basis the solutions for mode I and mode II stress

intensity factors KI and KII for each specimen geometry have been obtained. Table 1

present equtions describing the stress components and SIF functions on both the upper

and lower crack flanks.

Subjects for numerical studies are central notched plate and compact tension-shear

specimen (Fig.1). All investigated configurations contain an internal crack of length 2a

for C N Sor a for CTS. The initial crack makes on angle α with the loading direction. By

changing α, different combinations of modes I and II are achieved. In the CTSα = 90º

correspond to pure modeI and pure modeII can be achieved when α = 0º. For the C N S

α = 90º correspond to pure modeI.

Figure 1. Central notched and compact tension shear fracture specimens

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