Determination of mixed-mode fracture characteristics due dynamic opening and in-plane shear cases

In fracture mechanics the crack propagation problem is mainly discussed for individual cases of deformation, i.e. opening and affecting with shear [1, 2]. However, in practice often mixed cases are encountered when the crack is affected by opening and shear stresses. Most of the fracture mechanics of crack instability theories are based on the idea of Griffith [2]. For pure-mode cases, it has been commonly accepted that fracture will occur when the corresponding stress intensity factor reaches its critical value. Stress state ahead of a crack is often of the mixed


Introduction
In fracture mechanics the crack propagation problem is mainly discussed for individual cases of deformation, i.e. opening and affecting with shear [1,2].However, in practice often mixed cases are encountered when the crack is affected by opening and shear stresses.Most of the fracture mechanics of crack instability theories are based on the idea of Griffith [2].For pure-mode cases, it has been commonly accepted that fracture will occur when the corresponding stress intensity factor reaches its critical value.Stress state ahead of a crack is often of the mixed type where both d I K and d II K are present.Practical engi- neering cracked structures are subjected to mixed mode loading, thus in general I K and II K are both nonzero, yet we usually measure only mode I fracture toughness IC K .In this cases we have the so-called cumulative effect of modes I and II.The mode I describes the opening and normal stress effect and the mode IIthe shear cases and shear stress effect [1][2][3][4][5].The determination of a fracture initiation criterion for an existing crack in mode I and mode II would require a relationship between and would be analogous to the between the two principal stress and yield stress (Fig. 1): Fig. 1 Mixed mode crack propagation under opening (left side) and in-plane shear (right side) fracture modes These tests become more important when dynamic effects arise because this far, dynamic fracture patterns are least examined in the fracture mechanics.The known works [6,7] consider not only the characteristics of fracture, i.e. dynamic stress intensity factors d I K and d II K , but also focus on the crack path, i.e. when the crack propaga-tion angle depends on both loads: opening and shear.Sih at al [8] proposed a mixed-mode criterion of fracture, which states, that the combination of mode I and mode II stress intensity factors present will cause crack initiation upon reaching some critical value IC K .This critical intensity of the local stress field is a material constant and not depends on geometry of specimen.Also Sih at al [9] discussed the dynamic counterpart of Griffith crack configuration.
The dynamic crack propagation behaviour has attracted extensive attention during the past decades [10].There are a number of experiments, theoretical models and simulations constructed and performed to understand the phenomena of dynamic fractures.Zhang at al investigated dynamic crack growth and branching of running crack under mixed-mode loading.
In order to predict the fracture loadings of cracked materials under the general mixed-mode state Chang at al [11] proposed general fracture criterion based on the concept of maximum potential energy release rate.
However, the obtained dependences show little representation of mechanical properties of materials, which determine the fracture process.Therefore the work is focused on the parameters of the material strength and fracture that allow easier assessment of the crack growth specimens depending on the complex stress condition in the tip of the crack.This would allow describing critical dangerous levels also in the general load case.
Unlike the static case, solution to the dynamic problem is more difficult to obtain.The effects of dynamic loading on the distribution of stresses around a cracklike imperfection have not received sufficient attention.The elasto-dynamic problems are fundamental interest in fracture mechanics.

Testing procedures
Loading the specimen with an inclined crack, i.e. pulling and affected by shear according to mode I and mode II (Fig. 2).
In the work [1] from maximum circumferential tensile stress theory for mixed modes is writing:    3) and ( 4), from the Eq. ( 3) we get: Upon inserting the Eq. ( 8) to Eq. ( 4), it follows: From the obtained Eq. ( 9 9) then it will be written as: from here we get: i.e. 0  d II

K
and it shows that in this case there is no shear.
We only have the case of opening , as evidenced by Eq. ( 8).
In order to evaluate different opening and shear influence on fracture, the experiments with steel plates under mixed-mode loading have been carried out.Specimen was embedded in swinging pendulum with special fixture and lifted to starting position (Fig. 4).Released pendulum swings through and strikes the specimen causing fracture.In the scale of impact tester the breaking energy V C are shown.Using specimens with different angles of initial cracks, mixed-mode loading are obtained.The experimental results under various mixedmode loading conditions are given in Table 1.
Impact test results (Table 1) are shown in Fig. 5.It should be mentioned that increasing initial crack angle increases the fracture energy.
Empirical equation which relates fracture energy where stress intensity factor IC K is for static loading.Em- piric formulas having impact strength characteristics can be expressed in terms of critical stress intensity factor d IC K [12]: In our case the critical stress intensity factor   which is presented in Fig. 6.
As can be seen from the graphs, the effect of stress intensity factor d II K increases with increasing initial angle of the crack.The ratio 2. The obtained test and calculation results show different effect of the opening and shear to fracture, and the presented to dependences allow to assess the effect in qualitative indicators.
3. Test and calculation results can be applied not only to cracks with a clear path of spreading, but also for bifurcations on the tip of the main crack, where a mixed opening and shear fracture develops.


is crack angle from the crack position perpen- dicular to the load; d I K , d II K are dynamic stress intensity factors in the opening (mode I) and in-plane shear (mode II) cases.

Fig. 2
Fig. 2 Specimen with initial inclined crack under tensionEvaluating the characteristics of material strength, from minimum strain energy density criteria[1] can be expressed as: system of Eqs. (

.
Specimens are made of S355 grade construction steel, with statitac modulus of elasticity 200 Size length  width  thickness of the pre- cracked specimens are respectively 3 width and 8 mm length ini- tial crack are made.This initial crack imitates fatigue crack.

Fig. 3
Fig. 3 Specimen with oblique angles slits every 5 o , starting from 0 o to 45 o Fig. 4 Impact tester

Fig. 5 3 .
Fig. 5 Breaking energy were used to make a graph of changes in the dynamic stress intensity factors

Table 1
Results of the impact testing