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The 9th International Symposium on NDT in Aerospace

8-10 November, 2017, Xiamen, China

Research on finite element modelling method for delamination damage of stitched composite materials

Yupeng ZHANG, Yinwei MA, Lei ZHANG, Dongliang QUAN

Beijing aerospace technology institute, Beijing, China

Corresponding author: Yupeng Zhang, e-mail: zhangyupeng209@163.com Abstract Stitched composite materials presents typical delamination damage under bending load, traditional numerical model and analysis method cannot describe the interlayer and stitched effect, let alone the crack formation and propagation. Based on the theory of cohesion and finite element method, a new numerical model has been established to explore the mechanical properties and crack mechanism of stitched composite, in which the influence of interlayer crack generation and propagation are specially considered. With the analysis of theory and numerical methods, the mechanical properties and crack mechanism of stitched composite are investigated, which provide a new method for the structure assessment. Keywords: Stitched composite materials, Finite element modelling, Crack generation and propagation, Structure assessment

1. Introduction The stitched composite material is the three-dimensional textile composite material which is formed by the introduction of the reinforcing fiber in the direction of the thickness by the suture technique based on the two-dimensional laminar composite. Stitched composites is different from other kinds of 3d textile composites, most of the fiber lie in the in-plane thickness direction, and the proportion is also quite small. Besides, the in-plane stiffness and strength is significantly higher than the thickness direction of performance, and the direction of the thickness of fiber can significantly improve performance between the layers, which have a good inhibitory effect in interlayer delamination[1]. The research of stitched composites mainly focus on theory and experiment. Abroad study of stitched composites are mainly concentrated in the experiment[2] while research in China mainly focus on mechanical performance mechanism which based on reasonable assumptions and theoretical analysis modelt3]. Some scholars suggest that the curving fibers are distributed by sines or cosines in a single cell[4], and the effects of suture parameters on the properties of the materials are studied and analysed in this paper[5]. Throughout the world, the finite element simulation of suture composites is relatively rare. The finite element simulation of the rope of the composite material can be divided into the following categories: Solid element, truss element or the combination of solid and truss element for the rope. The structural correction parameters are obtained by a large number of suture tests [6].

Fig.1 Solid element simulation for the suture

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The 9th International Symposium on NDT in Aerospace

8-10 November, 2017, Xiamen, China

Fig.2 Truss element simulation for the suture

Based on the theory of cohesion and finite element method, in this paper, a new numerical model has been established to explore the mechanical properties and crack mechanism of stitched composite, in which the influence of interlayer crack generation and propagation are specially considered. With the analysis of theory and numerical methods, the mechanical properties and crack mechanism of stitched composite are investigated, which provide a new method for the structure assessment.

2. Finite element modelling of stitched composite The stitched composite is composed of laminated plates and stitches, and the common sewing patterns are shown in fig.3. The materials are composed of matrix and fiber, which are considered by the detailed mechanics of composite materials.

Fig.3 Stitched composite diagrammatic drawing Fig.4 Stitched composite analytical model

In normal circumstances, suture are evenly spaced. When stitching at 90 ° insert fiber, fiber is extruded by suture. The surface layer fiber distribution is approximately sinusoidal periodic distribution[4], which can establish the analytical model of stitched composite under bending load, as shown in figure 4. In this figure, the y direction is the direction of sewing needle, which represents the direction of sewing. The x direction is the direction of layer fiber, and the suture is inserted into the vertical plane. With the use of this analytical model, an analytical calculating process is established for evaluating the equivalent elastic properties of stitched composite material [5]. Considering the above theoretical analysis model, we find that the fiber is more complicated in the neighbourhood of rope, and the fiber is pushed out by the suture. The experimental results show that the mechanical properties of the composites are mainly caused by the bending deformation of the fibers[7], as shown in figure 4. Therefore, while establishing the finite element model of stitched composite, an elliptical area was cut out near the pin of the composite plate, and the properties of the substrate material were given to this area to simulate the influence of the insertion suture on the distribution of the fiber, and truss element is used to

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The 9th International Symposium on NDT in Aerospace

8-10 November, 2017, Xiamen, China

simulate the rope. With the combination of these two methods, the finite element model can better reflect the actual situation of the composite materials, as shown in figure 5.

Fig.5 Finite element model of stitched composite

3. Mechanical property analysis of stitched composite

3.1 The theoretical calculation of stitched monolayer plate

According to the theory introduced by Gui.etc [5], the change of material parameters after sewing can be get in the way of analytic solutions. The model is used for glass-reinforced plastics. The basic material parameters are: The matrix, Em = にぱどどMPa,νm = ど.ぬの. The fiber, Ef = ぱにはどどMPa，νf = ど.なひば，Gf = ぱどどどMPa，and the fiber content is 60%. The fiber is sewed vertical to the ply, the suture parameters are: stitch length, p = ぬmm. The row distance, q = のmm. The seam radius, r = ど.なmm. The analytical solutions are as follows.

Table 1 Comparison of elastic modulus E掴 E槻 Ν掴槻 G掴槻 stitched (MPa) のどねには はぱばね.ぬ ど.にはぬの にのはね.ひ

3.2 Finite element modeling of stitched monolayer plate

With the method of upper section, the finite element simulation of stitched monolayer plate is carried out. The plate is 20mm long, 12mm wide and 0.15mm thick, with 16 pinholes, as shown in the following figure.

Fig.6 Finite element model of stitched monolayer plate

The following describes the method of calculating the elastic modulus in the x direction of the monolayer plate. The left side is fixed, while the right side is applied with pressure � =−層宋���. The deformation of displacement is different everywhere, however, as we are more concerned with the overall deformation, so only the average displacement of the right side is needed to evaluate the elastic modulus. The strain of the model then can be calculated according to the average value of the change in the x direction. �� = ��

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The 9th International Symposium on NDT in Aerospace

8-10 November, 2017, Xiamen, China

In the same way, the elastic modulus in the y direction can also be get, the final calculation results are shown in the following table.

Table 2 Finite element calculation results STRETCH SIMULATION IN X DIRECTION STRETCH SIMULATION IN Y DIRECTION

Average displacement of nodes at などmm position

に.などばE − どぬ mm Average displacement of nodes at はmm position

ひ.なのねE − どね mm

Average displacement of nodes at 15mm position

ぬ.なのぱE − どぬ mm Average displacement of nodes at ひmm position

な.ぬはばE − どぬ mm

Average displacement of nodes at 20mm position

ね.にどぱE − どぬ mm Average displacement of nodes at なにmm position

な.ぱぬはE − どぬ mm

Average Strain � に.などのE − どね 平均应变� な.のにのE − どね E淡 ねばねひの.にの MPa E湛 はののひ MPa

Table 3 Errors correlation

THEORY RESOLUTI

ON FINITE ELEMENT

SOLUTIONS ERROR E淡 のどねには MPa ねばねひの.にの MPa の.ぱ% E湛 はぱばね.ぬ MPa はののひ MPa ね.は%

As can be seen from the above table, the finite element solution is very close to the theoretical solution, and results shows that the finite element simulation results are smaller than the theoretical ones, whether E淡 or E湛. The reason for this phenomenon is that in theoretical analysis, the fibrous material near the foot of the needle is pushed by the suture out to the adjacent unit and still exists in the layer. While the finite element modelling is to remove the influence of the fiber material on the single layer in the vicinity of the pin, resulting in the weakening of the overall material performance. However, from the results of the error analysis, the modelling method can be used to simulate the suture structure accurately, which is a new and innovative simulation method.

3.3 The calculation results under different factors

Based on the above analysis model, the paper focuses on the influence of the factors such as the pretension force of the suture, the elastic modulus of the suture and the density of suture on the overall performance of the stitched monolayer plate

3.3.1 The influence of pretension force of the suture

Using the above finite element model, the pretension force of � = −����� was applied to the suture in the method of cooling, and the change of material performance was compared.

Table 4 Calculation results considering pretension force of the suture STRETCH SIMULATION IN X DIRECTION STRETCH SIMULATION IN Y DIRECTION

Average displacement of nodes at などmm position

に.なひばE − どぬ mm Average displacement of nodes at はmm position

ひ.なばひE − どね mm

Average displacement of nodes at 15mm position

ぬ.なののE − どぬ mm Average displacement of nodes at ひmm position

な.ぬばなE − どぬ mm

Average displacement of nodes at 20mm position

ね.ににはE − どぬ mm Average displacement of nodes at なにmm position

な.ぱねはE − どぬ mm

Average Strain � に.ななはE − どね 平均应变� な.のぬどE − どね E淡 ねばなのば.のの MPa E湛 はのぬね.ぬば MPa

WITHOUT PRETENSION LOAD WITH PRETENSION LOAD E淡 47495.25 MPa 47157.55 MPa E湛 6559 MPa 6534.37 MPa

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The 9th International Symposium on NDT in Aerospace

8-10 November, 2017, Xiamen, China

According to the analysis results, pretension force of the suture has little effect on the overall performance of the stitched monolayer plate.

3.3.2 The influence of the elastic modulus of the suture

The elastic modulus of suture was changed from 2800MPa to 72800MPa, and the influence of elastic modulus of suture was simulated on the overall elastic modulus of suture structure.

Fig.7 Results of different elastic modulus of the rope

Elastic modulus of the rope has little effect on the overall �� values of the stitched monolayer plate, but with the increase of stitching modulus, the longitudinal modulus of suture plate tends to increase, and the increase is more and more gradual.

3.3.3 The influence of the density of suture

In order to compare stitch density effect on the elastic modulus of stitch composite, the stitching density of 4*4, 3*3, and 2*2 is calculated respectively. The finite element model is shown in figure 8.

Fig.8 Finite element model of different stitching density

Table 5 Calculation results of different density of suture STITCHING DENSITY に ∗ に ぬ ∗ ぬ ね ∗ ね E淡岫MPa岻 ねひばなぱ.どね ねぱぱなぱ ねばねひの E湛岫MPa岻 ははねの.どひ ははなば.ひ はののひ

Combined with the above data analysis, when the sewing direction is perpendicular to the direction of the layer fiber, the horizontal(x direction) and longitudinal(y direction) modulus gradually decrease with the increase of the suture density, and the decrease in longitudinal modulus is not significant.

4. Analysis of delamination damage for stitched composite

4.1 Introduction to the cohesion layer

The cohesive element in abaqus can be used to simulate delamination failure for composite efficiently, it support multiple failure criteria which includes Quade Damage, Maxe Damage, Quads Damage, Maxs Damage。

Quade Damage is the second nominal strain criterion: when the square sum of the nominal strain ratio is equal to 1, the damage initiates.

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The 9th International Symposium on NDT in Aerospace

8-10 November, 2017, Xiamen, China

2 2 2

0 0 01n s t

n s t

Maxe Damage is the maximum nominal strain criterion: when any nominal strain ratio reaches 1, the damage initiates.

0 0 0max , , 1n s t

n s t

Quads Damage is the second nominal stress criterion: when the nominal strain ratio of each direction is equal to 1, the damage initiates.

2 2 2

0 0 01n s t

n s t

t t t

t t t

Maxs Damage is the maximum nominal stress criterion: when any nominal stress ratio reaches 1, the damage initiates.

0 0 0max , , 1n s t

n s t

t t t

t t t

4.2 Size and material parameters of finite element model

Based on the four-point bending experiment, a composite laminated plate is established by using the method of solid layered modelling. The model from bottom to top is titanium alloy bottom plate, rubber layer, underlayer covering layer, thermal barrier, upper layer. Titanium alloy dimensions are はどどmm × ばどmm × のmm，E = などぱGPa，ν = ど.ぬね. The size of the rubber layer is ぬどどmm × はどmm × ど.のmm，E = なMPa，ν = ど.の. The yield criterion of cohesion connection layer adopts the Quads Damage criterion，The strength parameters are as follows:

Table 6 Quads damage criterion parameters

Table 7 Fracture toughness of cohesion layer

The sutures were transverse suture, and the stitching density was 15mm:

Fig.9 Finite element model of the suture

The parameters of the suture are as follows: Table 8 parameters of the suture � � Radius of stitching

75GPa 0.24 1mm

Normal Stress First Direction Stress Second Direction Stress 0.04MPa 0.09MPa 0.09MPa

�I� �II� �III� ど.どなN/mm ど.どぬN/mm ど.どぬN/mm

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The 9th International Symposium on NDT in Aerospace

8-10 November, 2017, Xiamen, China

4.3 Four - point bending numerical simulation

4.3.1 Calculation results under compression load

According to the above structure size and material parameters, the analysis model is established, and the simulation results are as follows:

Fig.10 Stress contour (left) and displacement contour (right) under the load of 2000N

Fig.11 Stress contour (left) and displacement contour (right) under the load of 4000N

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The 9th International Symposium on NDT in Aerospace

8-10 November, 2017, Xiamen, China

Fig.12 Stress contour (left) and displacement contour (right) under the load of 10000N

4.3.2 Delamination damage contour

Amplified the deformation factor and then we get a clear observation of delamination damage of the composite.

Fig.13 Delamination damage contour under the load of 2000N

Fig.14 Delamination damage contour under the load of 4000N

Fig.15 Delamination damage contour under the load of 10000N

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The 9th International Symposium on NDT in Aerospace

8-10 November, 2017, Xiamen, China

4.3.3 Damage contour of the cohesion layer

SDEG>0 indicates that the stress of the cohesive element reaches its ultimate strength and the structure has begun to damage. SDEG>0 indicates that the cohesion layer is completely destroyed and can no longer bear the load, these “dead” elements are deleted from the model.

Fig.16 Damage contour of cohesion layer under the load of 2000N

Fig.17 Damage contour of cohesion layer under the load of 4000N

Fig.18 Damage contour of cohesion layer under the load of 10000N

Fig.19 Final interface layer disruption diagram (front view)

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The 9th International Symposium on NDT in Aerospace

8-10 November, 2017, Xiamen, China

4.3.4 Results comparison between stitched and unstitched

Fig.20 Damage contour of cohesion layer under the load of 2000N:stitched(left),unstitched(right)

Fig.21 Damage contour of cohesion layer under the load of 4000N:stitched(left),unstitched(right)

Fig.22 Damage contour of cohesion layer under the load of 10000N:stitched(left),unstitched(right)

4.4 Results summary

Table 9 Maximum deflection of titanium alloy bottom plate Load 匝宋宋宋� �宋宋宋� 層宋宋宋宋�

Experiment:���� など − なのmm にどmm のどmm

Calculation results for stitched composite：����

など.はのmm にな.ぱにmm のな.はのmm

Calculation results for unstitched composite: ����

なば.ぱぱmm ぬは.ばのmm ばね.なばmm

Table 10 Displacement of the punch

Load 匝宋宋宋� �宋宋宋� 10000N

Experiment:���� ねmm ぱmm no record

Calculation results for stitched composite：����

ね.のmm ひ.なmm 21.3mm

Calculation results for unstitched composite: ����

は.ねmm なぬ.どmm 25.8mm

4.5 Summary

In this section, the delamination damage and crack propagation of the stitched composite material under the bending deformation of four points are studied from finite element calculation, and the summary is as follows: 1. In the comparison of the result between stitched and unstitched, it is obvious that the suture

play an important in the inhibition of delamination. 2. The calculation results give the initial position and the extension direction of the damage

between the layers, and the key arrangement of the seams in this area can be very good in inhibiting the overall delamination damage of the composite.

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The 9th International Symposium on NDT in Aerospace

8-10 November, 2017, Xiamen, China

3. The analysis results of the improved calculation model are basically in line with the experiment, the accuracy of the proposed model is validated, and the new way of thinking is presented for the further analysis of the mechanism.

5. Conclusion In this paper, based on the theory of cohesion and finite element method, a new numerical model has been established to explore the mechanical properties and crack mechanism of stitched composite, in which the influence of interlayer crack generation and propagation are specially considered, the shortcomings of the existing simulation methods are made up. The finite element calculation is compared with the theoretical calculation, and the experimental research is also verified with the simulation. The conclusions are as follows: 1. An innovative stitch structure simulation scheme is put forward, which makes up the defect

of the existing simulation methods. The theoretical solution and finite element solutions match well, which proves the accuracy of the scheme.

2. The influence of the pretension force, the elastic modulus and the density of suture on the overall performance of the stitched composite has been researched. a. Pretension force of the rope has little effect on the overall performance of the suture

laminated plate. b. Elastic modulus of the rope has little effect on the overall �掴 values of composite, but

with the increase of elastic modulus, the longitudinal modulus of composite tends to increase, and the increase is more and more gradual.

c. When the sewing direction is perpendicular to the direction of the layer fiber, the horizontal(x direction) and longitudinal(y direction) modulus gradually decrease with the increase of the suture density, and the decrease in longitudinal is not significant.

3. The delamination damage is studied, and the important role of suture in the inhibition of delamination is fully demonstrated by comparison with the unstitched laminated plates.

4. The calculation results give the initial position and the extension direction of the damage between the layers, which provides and a new way of thinking for the further analysis of the mechanism.

References

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2. Macander A B, Crane R M, Camponeschi E T. Fabrication and mechanical properties of multidimensionally (XD) braided composite materials[C]//Composite Materials: Testing and Design (Seventh Conference). ASTM International, 1986.

3. 魏玉卿 . 缝纫复合材料细观结构表征及面内力学性能的理论和模拟 [D].Ц海大学,2008.

4. Mouritz A P, Cox B N. A mechanistic approach to the properties of stitched laminates[J]. Composites part A: applied science and manufacturing, 2000, 31(1): 1-27.

5. 桂良进, 范子杰, 陈宗渝,等. 缝纫层合板的本构关系研究(I)--缝纫单层板有效弹性常数分析[J]. 复合材料学报, 2002, 19(1):95-100.

6. 燕瑛,韩凤宇,杨东升,刘兵山. 缝合复合材料弹性性能的Х维有限元细观分析与试验验证[J]. 航空学报,2004,03:267-269

7. M. Grassi, X. Zhang Prediction of stiffness and stress in fiber reinforced composite laminates. Composites Part A: Applied Science and Manufacturing.2002