Issue 75

D. I. Vichuzhanin et alii, Fracture and Structural Integrity, 75 (2026) 220-237; DOI: 10.3221/IGF-ESIS.75.16

The maximum strain is localized on the specimen–die interface at point A (fig. 17 d). However, most probably, fracture is initiated in the central part of the specimen (point B in fig. 17 d) since a more unfavorable stress state occurs here (fig. 18). The Lode–Nadai coefficient is close to zero at both points.

D IAGRAMS OF ULTIMATE STRAIN ENERGY DENSITY ( FRACTURE LOCI )

S

f W is used as the quantitative parameter characterizing the limiting state of epoxy resin in

train energy density

cohesive failure:

*



eq

     eq eq eq d

 

W

(9)

f

0

where *

eq  is ultimate strain at the site of failure.

f W for each material depends on the stress state characterized by the totality of the parameters k and   ,

The value of

f W must be determined in experiments

as well as temperature and strain rate. Rigorously, to construct the fracture locus,

  . However, it follows from the above dependences that the stress state is hardly

conducted at constant values of k and

invariable during testing; therefore, the quantitative dependence   , f W k   can be established only by using the averaged values of the stress parameters or by the identification procedure. The latter way is used in this study. Strain energy density * W at the crack initiation site is evaluated from the simulation of the testing process with account taken of the stress-strain history. The values of * eq  and * W reached at the site of failure and averaged from the simulation results are shown in Tab. 2.

Reinforced epoxy resin

Pure epoxy resin

Specimen, type of testing

T , ºC

* eq 

* eq 

* W , MJ/m 3

* W , MJ/m 3

25 -50 25 -50 25 -50 25 -50 25 -50 25 -50

0.052 0.04

4.65 4.14

0.047 0.023 0.033 0.034 0.529 0.07 0.029 0.024

3.38 1.53 1.31 3.23

Cylindrical, compression

Bell-shaped, tension

106.83 13.63

Bell-shaped, compression

0.037 0.022 0.025 0.047 0.078 0.079 0.18

2.74 1.34 4.41 5.63 8.07 11.7

1.44 1.63

Thick-walled cup, dishing

2 S  mm,

2 R  mm,

30   º

Plane shear

3 R  mm,

2.5 S  mm,

50   º

Plane shear

25

21.13

5 S  mm,

2 R  mm,

80   º

Plane shear

-50 Table 2: The data for identifying the dependence



 ,  

f W f k 

.



 ,  

f W f k 

As the objective function for the identification of the dependence

, the criterion for the failure of the linear

model of material damage  under deformation is used in the following interpretation:



eq

dW W

0 

 



(10)

1

f

232