Multi resolution defect transformation of the crack under different angles

International Journal of Research in Engineering and Science (IJRES)
ISSN (Online): 2320-9364, ISSN (Print): 2320-9356
www.ijres.org Volume 3 Issue 8 ǁ August. 2015 ǁ PP.20-24
www.ijres.org 20 | Page
Multi resolution defect transformation of the crack under
different angles
Gao Kun1
, Chen Hao2
, Zhang Shengwei, Duan Yu, Zhang Wen-Ping
Correspondence should be addressed to Chen Hao
1(College of Automotive Engineering, Shanghai University Of Engineering Science, Shanghai 201620China)
2
(College of Automotive Engineering, Shanghai University Of Engineering Science, Shanghai 201620China)
ABSTRACT : It is used to analyze the crack of different angles by the method of finite element. In the
same material, the same crack is applied different angles, crack with 15 degree Angle differences, and
applying Ⅰ type load on the material. The effective elastic modulus under the different angles of
crack are obtained by finite element. With comparative judgment method, it provides the relationship
between the modulus of elasticity and crack different angles, and a method crack material defects of
transformation. On based on the transformation of energy equivalent principle, there are a lot of
crack defects of materials for different degrees of defects, so as to simplify the material crack, provide
a simple way for material fatigue analysis.
Keywords –multiresolution;material defect;elasticity modulus
I. INTRODUCTION
The most parts in mechanical engineering are under cyclic loading, so the cycle load is a major cause of
leading to fatigue damage. In general, for high cyclic fatigue, Material of stress level is far less than the yield
strength of its own and therefore fatigue damage of sudden, so often with huge property losses and casualties.
There are two main types of research method of fatigue life, the kind of research method is based on damage
mechanics and fracture mechanics; Another is to use s-n curve to predict the fatigue life. The former could not
accurately the fatigue process of material defects, so the feasibility is poor; the latter need to do a lot of fatigue
life test, wasting time and energy. The new method for fatigue life prediction of mainly on the material defects
to simplify classification. For example, The GongL, Beijing University of Technology, on the labview platform
is presented in this paper. a intelligent recognition system of defects, but the accuracy is not high; Xue-zhi Yang,
hefei industrial university, China put forward a minimum classification error small potter of the textile defects
classification research, but this method mainly is in textiles, limitations. At the university of Michigan, ShenJie,
different defect levels of transformation method is put forward, Mainly for the approximation of the triangle,
circle, square defects,, using the finite element simulation and numerical analysis method to the simplification of
different levels of defects. However, no study of crack configuration of different angles, this paper mainly aims
at this problem, the different point of view of limited analysis of crack, determine the crack under different
angle of effective elastic modulus of the material.
II. MULTIRESOTION MOTHEDS
2.1The defect of multiresolution transformation
In practical engineering, there are a large number of defects for after long-term working components, the
main defects as crack, distribution of irregularity. These cracks distributed from microscopic to macroscopicIn
order to realize the material,multi-resolution damage method need an equivalent transformation method, makes
different levels of material defects contact with each other, and find the effective elastic modulus of materials
where there is injury.Taking the properties of the material in the cyclic loading into consideration.
Transformation rules of material defects are shown in Figure 1, assumes that the material has all sorts of
different levels of flaw, in one way, the first to use material of the initial elastic modulus E0. Step by step to
estimate the damage of material, the effective elastic modulus of E1was finally determined. Again on the basis
of the effective elastic modulus of E1,it is estimatedfor the material damage of secondary cracks, eventually to
determine the effective elastic modulus of E2. Another method, on the basis of the original all defects, and
estimate the damage of materials, directly in the original are determined on the basis of elastic modulus E0
material effective elastic modulus of E3.

Multi resolution defect transformation of the crack under different angles
Eventually it is determined for the elastic modulus of E2 and E3, respectively under the two kinds of
methods to find the effective young's modulus. We also need compare the gap between the two
2.2Numerical analysis of multi resolution
The above example is only two levels of the classification of the crack under simplified, whether classify
can simplify between cracks, the heaviest is that if damage conversion is effective. The most crucial step is that
a multi-scale damage mechanics model is set up. We assume that: the different levels of complementary energy
of elastic mechanics modelis expressed by the following
𝑊 𝑒
𝜎 𝐷 𝑖
, 𝐷𝑖 =
1
2
𝜎 𝐷 𝑖
𝑇
：𝐶 𝐷 𝑖
−1
：𝜎 𝐷 𝑖
，i = 0，1，，，n (1)
We
()——a complementary elastic energy，
Di——a damagetensor that represents the extent of damage accumulated from level 1 to leveli，
T——the transpose of a matrix，
σDi
——a stresstensor at damageDi，
CDi
−1
——the inverse of an effective stiffnesstensor，
There is the following special case:in whichC−1
is the inverse of a stiffness tensor at damage D0=0.CDi
−1
=
C−1
，（2）
We also assume that the equivalence of complementary energy takes thefollowing incremental form:
𝑊 𝑒
𝜎 𝐷 𝑖+1，𝐷𝑖+1 = 𝑊 𝑒
𝜎 𝐷 𝑖+1
，𝐷𝑖
=
1
2
𝜎 𝐷 𝑖+1
𝑇
：𝐶 𝐷 𝑖
−1
：𝜎 𝐷 𝑖+1
=
1
2
𝜎 𝐷 𝑖
𝑇
： 𝑀 𝑑𝐷𝑖
𝑇
：𝐶 𝐷 𝑖
−1
：M 𝑑𝐷𝑖 ：𝜎 𝐷 𝑖
（3）
σDi+1
——The effective stress tensor in the Di+1, To solve the equations as follows:
𝜎 𝐷 𝑖+1
= M 𝑑𝐷𝑖 ：𝜎 𝐷 𝑖
，（4）
d𝐷𝑖 = 𝐷𝑖+1 − 𝐷𝑖，i = 0,1，，n − 1（5）
The equation expressed the material defect ofmulti-resolution transformation rules. It is mainly used for
the different levels material defects to be homogeneously processed.
III. FINITE ELEMENT ANALYSIS OF CRACK DEFECT DISCUSSION
3.1Sample simulation parameters
The finite element software is used in the simulation of ABAQUS, and the stress singularity at the crack tip
of ABAQUS has a strong analytical ability, which can show the crack propagation phenomenon. The specific
parameters of the sample are shown in Table 1
E1 E2E0
E3
Fig. 1 defects into law

Table 1
The simulation test
specimen
Parameter Data
Specimen size（L×B） 100×40（mm）
Applying external force
（kPa）
100
Crack sizes (L) 10（mm）
Crack angle (degree) 15
Elasticity modulus 3×107
Poisson ratio 0.3
3.2Analysis and calculation of elastic modulus in finite element method
This Due to the material itself inherent attributes, there are some inevitable defects on materials. In the
machining process of parts, there are different length and arrangement of cracks. As shown in the following
diagram: the crack is rotated counterclockwise, and the angle of each rotation is 15 degrees, and the straight line
between the figures is preset. Boundary conditions: The sample boundary in the direction of Y axis is fixed,
allowing the displacement in the X axis direction. The stress and strain are solved under different conditions.
Due to the limitations of the finite element software, we can only get the stress or strain of a single node or
element, so we need to solve the average stress and average strain of the whole material.
σ =
F1+F2+⋯
A
（6）
ε =
d1−d3 + d2−d4 +⋯
nL
（7）
σ：mean stress,
ε：mean strain,
Fi：the force of node i,
n：node number,
3.3Calculation results and discussion of elastic modulus
Finite element software can be on the structure of stress and strain analysis, using the finite element
software general after pre-processing, solution and post treatment process by visualization module in the post
processing of the extracted n nodes stress and displacement components, to approximately calculate the
presence of different defects of the elastic modulus of materials. The specific analysis process as shown in
Figure2
Fig. 2 Analysis of elastic modulus in finite element method
Model
Mesh
Solution
Boundary
conditions and
load
Post-
processing
Multi
node
stress
and
strain
Solution
of
elastic
modulus

It in Figure 3shows values for the elastic modulus under different angles, wherein E1 represents a crack
perpendicular to the external load, E2 load and crack angle is 15 degrees, and so on. From the table available,
when cracks are present at different angles, the elastic modulus of gradual change. Perpendicular to the crack
and the external load and change of its elastic modulus value maximum, the influence on the properties of
materials maximum. With the increase of the angle, trend of elastic modulus decreases, finally tends to be
stable, From Figure 4, the difference in elastic modulus is within the allowable range of 10%
Fig. 3Comparison of elastic modulus in the change of crack angle
.
Fig .4Modulus difference ratio
IV. CONCLUSION
For fatigue analysis, due to the irregularity of the crack, it is almost impossible to adopt accurate
classification of crack. Finite element simulation through the cracks of different angle, we can summarize
influence of edge crack of elastic modulus is greater than the median crack; influence of cracks on the elastic
modulus is greater than a single crack; crack in different angles, elastic modulus with the change. The vertical
0
5000000
10000000
15000000
20000000
25000000
30000000
35000000
0 degrees 30 degrees 45 degrees 60 degrees 90 degrees
method 1
method 2
0.0000%
0.5000%
1.0000%
1.5000%
2.0000%
2.5000%
3.0000%
3.5000%
0 degrees 30 degrees45 degrees60 degrees90 degrees
Difference ratio
Difference…

effects of the elastic modulus of the material to a load ofthe crack. It has important significance for predicting
fatigue life and the simplified finite element model,.
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Multi resolution defect transformation of the crack under different angles

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