Damage evolution in delaminated woven fabric E-glass/epoxy composite plates under transverse static patch loading

Abstract

Delaminations present in a laminated composite structure can grow under different loading conditions, thus further weakening the structure. Along with this, initiation and propagation of damages within the layers can take place because of in-plane stresses. Studies have been presented on damage evolution in delaminated woven fabric composite plates with initial delamination under pressure loading, normal to the plane of the plate, distributed over a small area. Delamination propagation has been studied using crack closure integral technique and finite element analysis. Initiation of failure of layers because of in-plane stresses has been studied using maximum stress failure criterion. Size and shape of the damage has been evaluated using the method presented and compared with the experimental results available in the literature.

Keywords

Delaminated plate in-plane damage delamination propagation crack closure integral technique contact element woven fabric composite

Introduction

Polymer matrix laminated composites made of unidirectional (UD) layers are being used for high performance applications during the past four decades. These materials are characterized by high specific in-plane stiffness and strength properties. Such materials have potential advantages when the loading is primarily in the plane of composite structures, but they are very sensitive to transverse loading because of the weak interfaces between the layers. Delaminations along the interfaces can cause severe structural degradation leading to reduction in stiffness and strength. The delamination present in a composite structure can grow under applied load, thus further weakening the structure. Assessment of the effect of internal damages such as delamination, matrix cracking and in-plane failure of layers on the performance of the composite structures is essential for their effective use.

Various damage modes in a composite structure under different loading conditions are matrix micro-cracking, debonding, lamina splitting, and delamination. On further loading, the in-plane damages can grow leading to fiber breakage and pullout. These are service-induced damages. Defects and the damages can be induced during maintenance. Dropping of a tool onto a composite part during routine maintenance can induce transverse low-velocity impact damages. Low-velocity impact can cause internal damages such as delamination, matrix cracking, and in-plane failure of layers in the interior of the composite structure and the surfaces may appear to be undamaged on visual inspection. Various damages can also be caused during manufacturing of composite structures. If such damages are undetected after the manufacture of the structure, or after the maintenance is complete, the composite structure would have internal damages during its service life. Delamination is one of the critical damage modes. Further, it can propagate during the service life of the structure.

Several methods are used in literature for the prediction of delamination growth such as:

Virtual crack closure technique (Abdullah et al., 2007; Buchholz, 1994; Chen et al., 1996; Irwin, 1957; Kamiya et al., 1998; Kruger, 2004; Lu and Liu, 1991; Pradhan and Chakraborty, 2000; Razi and Kobayashi, 1993; Rybicki and Kanninen, 1977).

Cohesive zone model (Barenblatt, 1962; Dugdale, 1960; Elmarakbi et al., 2009; Hu et al., 2007, 2008; Overguaard et al., 2010; Sridharan, 2008; Turon et al., 2006; Wager and Balzani, 2008).

Spot weld method (Fleming and Fasanella, 2000; Kerth et al., 1996; Kohlgruber and Kamoulakos, 1996).

J-integral method (Rice, 1968).

Virtual crack extension method (Hellen, 1975).

Stiffness derivative method (Parks, 1974).

Virtual internal bond (VIB) method (Aymerich et al., 2008; Gao and Klein, 1998; Klein and Gao, 1998).

Extended finite element method (Nicolas et al., 1999; Toshio and Hiroshi, 2010).

Transverse loading induced delaminations in laminated composites has been investigated by many researchers (Abdullah et al., 2007; Aymerich et al., 2008; Doxsee et al., 1993; Elmarakbi et al., 2009; Hu et al., 2007, 2008; Kamiya et al., 1998; Lu and Liu, 1991; Overguaard et al., 2010; Pradhan and Chakraborty, 2000; Razi and Kobayashi, 1993; Stout et al., 1999; Turon et al., 2006; Wager and Balzani, 2008). These studies are on laminated composites made of UD layers.

During transverse loading of laminated composite plates, the major damage modes are delamination initiation and propagation and in-plane failure of different layers. Possible in-plane failures of different layers along with delamination propagation were not considered in the above-mentioned studies.

Lu and Liu (1991), Razi and Kobayashi (1993), Kamiya et al. (1998), and Pradhan and Chakraborty (2000) studied delamination growth based on strain energy release rate consideration. Abdullah et al. (2007) used eight-noded solid elements for the study of initiation of delamination based on virtual crack closure technique. They used the model in double cantilever beam (DCB) test and numerical results were validated with the experimental results.

Turon et al. (2006) used a delamination criterion in finite element modeling for different test cases such as DCB, end notch flexure (ENF), mixed mode bending (MMB) tests, and skin-stiffener de-bonding test. The numerical results were validated with the experimental results. Wager and Balzani (2008) studied the delamination and skin-stringer separation using finite element method using cohesive interface elements. DCB test was used to simulate the delamination and skin-stringer separation. Overgard et al. (2010) proposed a methodology for the analysis of large three-dimensional (3D) laminated composite structures undergoing geometric and material instabilities. Propagation of multiple delamination fronts and multiple crack formations were tracked using the localized sub-plane control method. Using the proposed method, a laminated composite wind turbine blade was studied. They observed that the results were comparable to the closed form solutions and experimental results.

Hu et al. (2007, 2008) studied both in-plane and interface damages under transverse loads for UD laminates. They used the cohesive interface model for delamination propagation and stress-based criterion for in-plane damage propagation. Hu et al. (2007, 2008) and Elmarakbi et al. (2009) studied damage initiation and propagation under quasi-static loading.

Aymerich et al. (2008) carried out 2D and 3D finite element analyses in ENF and MMB tests using VIB approach in UD laminates containing a pre-existing delamination in the middle plane of the beam under quasi-static loadings.

Doxsee et al. (1993) studied experimentally delamination growth in symmetric cross ply laminates subjected to transverse quasi-static and low-velocity impact loading. Stout et al. (1999) studied the damage development in UD layers under quasi-static loading using four-point bend test.

Lammerant and Veropoest (1996) observed that the damage initiated in the bottom most layers in the form of matrix cracking/lamina splitting under transverse loading in the case of laminated composites made of UD layers. Further, they observed that it progressed to the nearest interface. Overall, it was observed that the damage pattern was of reversed pine tree type. Damage initiation was taking place in the bottom most layer because of lower transverse tensile strength.

Chen et al. (1996) studied the delamination growth in composite laminates under in-plane loading. Rebiere and Gamby (2004) studied the occurrence and influence of various damage modes like transverse and longitudinal cracking and delamination in cross ply laminates for tensile loading along 0° direction.

Toshio and Hiroshi (2010) developed a code based on extended finite element method with shell elements for thin-walled structures. The nodes on the interface of thin-walled structure were enriched in order to model the delamination. The method was applied to buckling analyses of a carbon fiber reinforced plastic laminate with delamination. Experimental validation was not presented.

Studies on transverse low-velocity impact induced delamination are available in various literatures (Baucom and Zikry, 2005; Baucom et al., 2006; Chio and Chang, 1992; Elmarakbi et al., 2009; Finn and Ye-Fei, 1993a, 1993b; Hu et al., 2008; Jih and Sun, 1993; Naik and Meduri, 2001; Siow and Shim, 1997; Wu and Springer, 1998). These studies were on laminated composites made of UD layers (Chio and Chang, 1992; Elmarakbi et al., 2009; Finn and Ye-Fei, 1993a, 1993b; Hu et al., 2008; Jih and Sun, 1993; Wu and Springer, 1998) and on woven composites (Baucom and Zikry, 2005; Baucom et al., 2006; Naik and Meduri, 2001; Siow and Shim, 1997). Baucom and Zikry (2005) studied the damage progression and energy absorption capability under repeated low-velocity impact loading in 2D woven, 3D orthogonally woven, and bi-axially warp knit composite systems. Further, Baucom et al. (2006) studied the damage accumulation due to repeated low-velocity impact loading in 2D woven and 3D orthogonally woven composites. The 3D systems showed unique damage, wider distribution of material damage and absorbed more energy compared to 2D systems. Both experimental and numerical studies have been carried out on 2D plain weave composite under quasi-static punch shear loading (Xioa et al., 2007).

Damage evolution in woven fabric (WF) composites without delamination under transverse-static loading is presented in Naik et al. (2003b). Typical experimental studies are presented for WF composites in Naik and Raju (2001) and Naik and Reddy (2002). The behavior of WF composites under transverse loading is not well studied.

Tian and Fu (2011) carried out studies on interfacial damage evolution for laminated composite plates under the action of transverse loads. Gornet and Ijaz (2011) developed a fatigue damage model to carry out simulation of the evolution of delamination in laminated composite structures. Tan et al. (2012) studied impact damage resistance and propagation of through-the-thickness stitched composites. Labeas et al. (2012) used progressive damage modeling for large-scale composite structures. Sub-modeling techniques were introduced to reduce computational time required.

The objective of this study is to find out delamination and in-plane failure evolution in a delaminated WF composite plate during pressure loading, normal to the plane of the plate, distributed over a small area. For this, a typical plain weave fabric composite with initial delamination has been analyzed. Because of the balanced in-plane properties, in-plane tensile failure of lower layers may not be the first mode of failure for WF composites. Also through-the-thickness normal stress is higher in the upper region of the composite plate during transverse loading. This can lead to possible delamination initiation in the upper region of the composite plate (Naik et al., 2000). Additionally, delamination can be caused anywhere in the plate because of manufacturing defects.

Considering these aspects, a central artificial delamination has been introduced in the upper region of a WF composite plate. During pressure loading, normal to the plane of the plate, distributed over a small area, the delamination can propagate further. Also, failure can take place within the layers because of in-plane stresses. Using the finite element analysis (FEA), the stress state has been evaluated throughout the composite plate. Delamination propagation studies have been carried out using the crack closure integral technique (Buchholz, 1994; Irwin, 1957; Kruger, 2004; Rybicki and Kanninen, 1977). Damage initiation studies within the layers have been evaluated using the maximum stress failure criterion (Jones, 1999). Delamination and in-plane failure evolution has been treated independent of each other in this study. Further, possible merger of these two modes of damages has been explained. Delamination and in-plane damage evolution at different loads and damage shapes and sizes have been determined. The predicted damage shapes and sizes have been compared with the experimental results available in literature. The studies have been carried out for a typical plain weave E-glass/epoxy composite laminate with a central delamination.

Stress analysis

3D linear elastic FEA software was used to find out the stress state in the composite plates. 3D eight-noded brick element was used in the analysis with three degrees of freedom at each node (u, v, and w). By taking symmetry into consideration, quarter plate analysis was carried out for this study with quarter plate dimension of 64 × 64 × 5 mm³. The thickness of the layers used for the experimental studies made of plain weave E-glass/epoxy was 0.2 mm. Such a specimen/laminate is referred to as GLE-12. Local–global discretization was used with a finer mesh near the loading point and relatively coarser mesh away from the loading point. Convergence study was carried out for the mesh size. Based on the convergence study, the discretization area for finer mesh was 20 × 20 mm², mesh size was 1 × 1 × 1 mm³ with aspect ratio of 1. The thickness of the element used was the same throughout the plate. A similar method was used for damage evolution studies in WF composites without delamination under pressure loading, normal to the plane of the plate, distributed over a small area (Naik et al., 2003b).

The co-ordinate system for the composite plate is shown in Figure 1(a). The cross-section of the composite plate is presented in Figure 1(b). Delaminated interface is indicated as interface I. It is 1 mm below from the top surface. It may be noted that there are 5 layers above the delaminated interface and 20 layers below the delaminated interface. Scheme of local–global discretization is given in Figure 1(c). Figure 1(d) presents the discretization of interface I and nodal positions. The boundary conditions for the quarter plate are as given below:

At	Simply supported	Clamped
x = 0	u ≠ 0, v = 0, w = 0	u = 0, v = 0, w = 0
x = L_x/2	u = 0, v ≠ 0, w ≠ 0	u = 0, v ≠ 0, w ≠ 0
y = 0	u = 0, v ≠ 0, w = 0	u = 0, v = 0, w = 0
y = L_y/2	u ≠ 0, v = 0, w ≠ 0	u ≠ 0, v = 0, w ≠ 0

Transverse central static patch loading: Load distribution

Transverse central static pressure loading, normal to the plane of the plate, distributed over a small area has been considered for this study. Separate experimental indentation studies have been carried out to study the contact area of indentation and the depth of indentation. In these studies, on a typical plain weave E-glass/epoxy laminate GLE-12, the loading tup had a tip radius of 6.5 mm, the unsupported area of the plates was 128 × 128 mm² with clamped boundary conditions. The permanent indentation on the upper surface of the laminate was studied after unloading the specimen. At transverse central patch loading of 4.0 kN, it was observed that the indentation had a spherical shape. The surface diameter of the indentation was observed to be 4 mm and the depth of indentation to be 0.5 mm. Elliptical load distribution was considered over the contact area with peak stress at the center. Accordingly, for a loading of 1 kN, the following distribution of load at different nodes has been considered for the quarter plate:

Node	Load (N)
1	40
2 and 4	60
3	70
5 and 9	10

A similar scheme was used for damage evolution in WF composites without delamination under transverse static pressure loading (Naik et al., 2003b).

Damage analysis

Using the 3D linear elastic FEA software and the boundary conditions explained, the nodal displacements and the stress state have been evaluated throughout the composite plate.

Maximum stress failure criterion (Jones, 1999) has been used for in-plane damage initiation studies. For tensile normal and shear stresses, failure initiation is defined by

\frac{σ_{1}}{X_{T}} = I, \frac{σ_{2}}{Y_{T}} = I, | \frac{τ_{12}}{S_{12}} | = I

(1a)

For compressive normal stresses, failure initiation is defined by

\frac{σ_{1}}{X_{C}} = I, \frac{σ_{2}}{Y_{C}} = I

(1b)

Here, σ₁, σ₂, and τ₁₂ are the induced in-plane stress components and X_T, Y_T, X_C_, Y_C, and S₁₂ the normal and in-plane shear strength values. I is in-plane failure function. The damage initiation takes place in the form of matrix cracking/lamina failure when the values of the in-plane failure function I just reaches unity. Any stress component can lead to initiation of in-plane failure.

Delamination propagation has been analyzed using fracture mechanics-based approach. FEA software has been used to obtain the stress distribution at the delamination front in the interface. The crack closure integral technique (Buchholz, 1994; Irwin, 1957; Kruger, 2004; Rybicki and Kanninen, 1977) has been used for the studies. Total strain energy release rate at the delamination front has been evaluated using the stress and crack opening displacement data. In this study, the delamination location has been taken to be in the upper half of the plate, i.e. in the compressive region. For such a case, the sub-laminate above the delamination has lesser thickness compared with the sub-laminate below the delamination. Hence, the vertical displacements (w) would be more for the upper sub-laminate compared with that for the lower sub-laminate. This would lead to node inter-penetration which is not a physical reality. To overcome this, contact elements have been used between the two halves of the composite plate within the delaminated region. This would ensure that there would not be node inter-penetration. Hence, through-the-thickness displacement in the delaminated region would be the same for both the halves of the composite plate. For such a case, there would not be Mode I fracture at the delamination front. It would be only Mode II fracture along the warp and fill directions and along 45° directions with respect to warp and fill. Along the other directions, it would be predominantly Mode II fracture with a possibility of Mode III fracture.

Delamination propagation takes place when the strain energy release rate computed exceeds the critical strain energy release rate. The delamination criterion used for the present case is

G_{II} \geq G_{II C}

(2)

For an applied transverse load, along with delamination propagation in the interfaces, in-plane failure of layers can also take place because of the in-plane stresses. For the complete understanding of damage evolution during transverse static patch loading, damage initiation within the layers and further growth because of in-plane stresses and delamination propagation in the interfaces because of through-the-thickness normal stresses and interlaminar shear stresses are monitored.

Results: Numerical studies on composite plates with initial delamination (specimen SP2a)

In this section, delamination and damage propagation studies have been carried out on a typical plain weave E-glass/epoxy laminate GLE-12. Considering the symmetry conditions, quarter plate analysis has been carried out with a central pressure load with the load distribution as explained earlier. Propagation of delamination at the interface is referred to as delamination propagation whereas propagation of in-plane damages within the layer is referred to as damage propagation.

The mechanical properties of laminate GLE-12 are given in Table 1. It is a symmetric and balanced laminate. Evolution of damage in plain weave fabric composites under on-axis uniaxial tensile loading and under on-axis uniaxial compressive loading is given in Ganesh and Naik (1996) and Naik et al. (2003a). Pure matrix block, transverse strand, and ultimate strand failures are the main stages during tensile loading whereas transverse strand and the ultimate strand failures are the main stages during compressive loading (Ganesh and Naik, 1996; Naik et al., 2001, 2002a, 2003a). Strength properties with respect to these stages are given in Table 1.

Table 1.

Mechanical properties of a typical plain weave E-glass/epoxy composite, GLE-12, $V_{f}^{0} = 0.44$ .

Elastic properties
$E_{11}$ (GPa)	$E_{22}$ (GPa)		$E_{33}$ (GPa)		$G_{12}$ (GPa)		$G_{13}$ (GPa)		$G_{23}$ (GPa)		υ ₁₂		υ ₁₃		υ ₂₃		ρ (kg/m³)
20.8	20.8		8.7		3.92		4.2		4.2		0.173		0.279		0.279		1808
Strength properties
X_T (MPa)		$Y_{T}$ (MPa)		$Z_{T}$ (MPa)		$S_{12}$ (MPa)		$S_{13}$ (MPa)		$S_{23}$ (MPa)		$X_{C}$ (MPa)		$Y_{C}$ (MPa)		$Z_{C}$ (MPa)
360		360		32		28		28		28		225		225		350
250^a		250^a										183^b		183^b
50^c		50^c

At pure matrix block failure; ^bat transverse strand failure; ^cat transverse strand failure.

Delamination propagation

For this study, with a plate of 128 × 128 mm² size and thickness of 5 mm, central delamination of 4 × 4 mm² at a distance of 1 mm from the top surface has been introduced, i.e. delamination size is 2 × 2 mm² for the quarter plate. Such specimens are referred to as SP2a. Delamination was introduced by removing nodal connectivity in the delaminated region.

The double plate modeling technique was used for introducing the delamination within the composite plate (Zheng and Sun, 1995). Within the delaminated region, the lower part of the plate has a thickness of 4 mm whereas upper part of the plate has 1 mm thickness. Within the delaminated area, nodal connectivity was removed. Outside the delaminated region, all the corresponding nodes of the upper and lower parts of the plate are merged. Since the thickness of the upper part of the plate is less than the thickness of the lower part of the plate, there can be node inter-penetration within the delaminated region. To overcome this problem, contact elements have been used within the delaminated region. Contact element CONTA 173 from ANSYS 13 was used for this analysis. Since the relative displacement between the upper and the lower layers was a very small quantity, frictional forces were not considered for this analysis.

Crack closure integral technique (Appendix 2) has been used for the analysis of delamination propagation. It involves calculation of strain energy release rate in two steps. In the first step, the stresses corresponding to the failure mode are calculated at the crack tip, i.e. stresses are calculated at the nodes corresponding to the crack tip. In the second step, the connectivity in the crack tip node is removed and the analysis is performed to calculate the relative displacements between the nodes whose connectivity has been removed. Then using the nodal forces from the stresses, and the nodal relative displacements, the strain energy release rate is calculated and compared with the critical values.

Delamination and damage propagation studies have been carried out with initial delamination of 2 × 2 mm² for the quarter plate at a distance of 1 mm from the top surface. For this arrangement, nodal connectivity is removed for nodes 1, 2, 3, and 4 within the delaminated region. Outside the delaminated region, all the corresponding nodes of the upper and lower parts of the plate have been merged. Specifically, considering the symmetry conditions within the quarter plate, nodal connectivity is removed for nodes 1, 2, and 3 for stress analysis and nodal connectivity is removed for nodes 1, 2, 3, 5, 6, and 7 for calculating nodal displacements. Such a scheme is referred to as Model-1. Different schemes of introducing the delamination are presented in Table 2. For Model-11, nodal connectivity is removed only at node 1 for stress analysis. In other words, the area of delamination is 1 × 1 mm² for the quarter plate.

Table 2.

Scheme of introducing delamination in 1/8th of the full plate.

Model	Nodal continuity removed at nodes
Model	For stress calculations	For displacement calculations
Model-1	1, 2, 3 (0.5266)	1, 2, 3, 5, 6, 7 (0.5304)
Model-2	1, 2, 3 (0.5266)	1, 2, 3, 5, 6 (0.5300)
Model-3	1, 2, 3, 5, 6 (0.5300)	1, 2, 3, 5, 6, 10, 11 (0.5316)
Model-4	1, 2, 3, 5, 6, 7 (0.5304)	1, 2, 3, 5, 6, 7, 10, 11, 12, 13 (0.5327)
Model-11	1 (0.5220)	1, 2, 3 (0.5266)

The quantity given within parentheses indicates central displacement in millimeter at a load of 1 kN for clamped boundary condition.

For a transverse central pressure load of 1 kN, nodal stresses at nodal positions 5, 6, and 7 are presented in global coordinate system for clamped boundary condition (Table 3). It may be noted that the behavior at nodes 2 and 4, 5 and 9, and 6 and 8 are similar. Further, to calculate the nodal displacements, nodal connectivity is removed at nodes 5–9 also. Based on this, nodal displacements are calculated. Nodal displacements are also presented in Table 3. Here u₁, v₁, and w₁ refer to the lower half of the plate whereas u₂, v₂, and w₂ refer to the upper half of the plate. The results are presented in Table 3 for nodal positions 5, 6, and 7. Since three nodes are forming crack tip, different types of removing nodal connectivity like removing only at two nodes and at three nodes can be considered. The details about various types of removing nodal connectivity are worked out and presented in Table 2.

Table 3.

Nodal stresses and displacements at interface I in a composite plate with a central delamination in global co-ordinate system.

Nodal position	Nodal stress, ith node (MPa)^a						Nodal displacement, ith node (mm)^b
Nodal position	$σ_{x}$	$σ_{y}$	$σ_{z}$	τ_xy	τ_yz	τ_xz	u ₁	u ₂	ν ₁	ν ₂	w ₁	w ₂
5	−59.38	−35.76	−19.56	−2.40	−5.26	−28.68	0.0050	−0.0026	0.0000	0.0000	−0.4940	−0.4940
6	−55.95	−40.04	−4.66	−6.90	−13.78	−22.37	0.0047	−0.0012	0.0026	−0.0005	−0.4920	−0.4920
7	−47.91	−47.91	−4.37	−6.39	−8.98	−8.98	0.0043	0.0012	0.0043	0.0012	−0.4860	−0.4860
5	−59.38	−35.76	−19.56	−2.40	−5.26	−28.68	0.0048	−0.0025	0.0000	0.0000	−0.4940	−0.4940
6	−55.95	−40.04	−4.66	−6.90	−13.78	−22.37	0.0048	−0.0012	0.0023	−0.0001	−0.4920	−0.4920
10	−63.50	−40.47	0.97	−10.00	−0.54	−1.31	0.0066	0.0011	0.0000	0.0000	−0.4840	−0.4840
11	−59.70	−41.95	−0.27	−2.51	−3.83	−11.36	0.0064	0.0018	0.0019	0.0011	−0.4830	−0.4830
10	−63.50	−40.20	0.84	−1.00	−0.54	−13.50	0.0070	0.0010	0.0000	0.0000	−0.4850	−0.4850
11	−60.00	−41.60	−0.24	−2.50	−4.02	−11.40	0.0065	0.0017	0.0023	0.0006	−0.4835	−0.4835
12	−41.60	−37.50	1.50	−1.44	−4.80	−5.00	0.0060	0.0030	0.0042	0.0017	−0.4805	−0.4797
13	−36.20	−36.20	0.62	0.11	−2.30	−2.30	0.0054	0.0034	0.0054	0.0034	−0.4760	−0.4751

Plate size: L_x = 128 mm, L_y = 128 mm, and L_z = 5 mm; material: GLE-12, clamped, and static load = 1 kN.

Before crack propagation and ^bafter crack has propagated up to (i + 1)th node.

It may be noted that the nodal stresses and nodal displacements in Table 3 are based on global coordinate system (x, y, and z). For the calculation of strain energy release rate at different nodal positions, stress and displacement information is necessary with respect to local coordinate system ( $x', y', z'$ ). In the present case, it may be noted that co-ordinates z and z′ coincide.

Using the transformation matrix (Chou, 1992), nodal stresses have been calculated with respect to local coordinate system (

x', y', z'

) at different nodal positions and are presented in Table 4. Nodal displacements are also presented in Table 4.

Table 4.

Nodal stresses and displacements at interface I in a composite plate after transformation with respect to given orientation.

Nodal position	Angle of rotation	Nodal stress, ith node (MPa)^a						Nodal displacement, ith node (mm)^b
Nodal position	Angle of rotation	$σ_{x'}$	$σ_{y'}$	$σ_{z'}$	τ_x_′_y_′	τ_y_′_z_′	τ_x_′_z_′	$u_{1}^{1}$	$u_{2}^{1}$	$v_{1}^{1}$	$v_{2}^{1}$
5	0.00	−59.38	−35.76	−19.56	−2.40	−5.26	−28.68	0.0050	−0.0026	0.0000	0.0000
6	26.56	−58.30	−37.70	−4.67	2.22	−2.32	−26.17	0.0054	−0.0013	0.0004	0.0001
7	45.00	−54.30	−41.52	−4.37	0.00	0.00	−12.70	0.0061	−0.0017	0.0000	0.0000
5	0.00	−59.38	−35.76	−19.56	−2.40	−5.26	−28.68	0.0048	−0.0025	0.0000	0.0000
6	26.56	−58.30	−37.70	−4.67	2.22	−2.32	−26.17	0.0053	−0.0011	0.0001	0.0005
10	0.00	−63.50	−40.47	0.97	−10.00	−0.54	−1.31	0.0066	0.0011	0.0000	0.0000
11	18.43	−59.40	−42.20	−0.27	3.52	−0.04	−12.00	0.0067	0.0021	0.0002	−0.0005
10	0.00	−63.50	−40.20	0.84	−1.00	−0.54	−13.50	0.0070	0.0010	0.0000	0.0000
11	18.43	−59.66	−41.94	−0.24	3.52	−0.21	−12.10	0.0069	0.0018	0.0003	0.0003
12	33.70	−41.67	−37.43	1.50	−1.34	−1.22	−6.82	0.0073	0.0035	0.0002	0.0003
13	45.00	−36.10	−36.10	0.62	0.00	0.00	−3.25	0.0076	0.0048	0.0000	0.0000

Plate size: L_x = 128 mm, L_y = 128 mm, and L_z = 5 mm; material: GLE-12, clamped, and static load = 1 kN.

Before crack propagation and ^bafter crack has propagated up to (i + 1)th node.

Nodal forces are calculated based on the nodal stresses. The area on which nodal forces are acting has been calculated proportionately based on the location of the nodes. This area is referred to as crack propagation area. For example, to calculate nodal forces at nodes 5, 6, and 7, crack propagation areas considered are (0.5 × 2) mm², 0.6 mm² and (0.4 × 2) mm², respectively, so that total area does not exceed the total crack propagation area. These nodal forces are presented in Table 5 for nodal positions 5, 6, and 7.

Table 5.

Nodal forces and strain energy release rates at interface I in a composite plate with a central delamination.

Nodal position	Nodal force (N)						Strain energy release rate (J/m²)
Nodal position	$F_{x'}$	$F_{y'}$	$F_{z'}$	$F_{x' y'}$	$F_{y' z'}$	$F_{x' z'}$	$G_{II}$
5	−29.69	−17.88	−9.78	−1.2	−2.63	−14.34	109.0
6	−34.98	−22.62	−2.80	1.33	−1.39	−15.70	87.7
7	−43.44	−33.22	−3.50	0.00	0.00	−10.16	49.5
5	−29.69	−17.88	−9.78	−1.2	−2.63	−14.34	104.6
6	−51.01	−32.99	−4.09	1.94	−2.03	−22.90	83.7
10	−31.75	−20.24	0.49	−5.00	−0.27	−0.66	3.6
11	−59.40	−42.20	−0.27	3.52	−0.04	−12.00	27.6
10	−31.75	−20.10	0.42	−0.50	−0.27	−6.75	40.5
11	−29.83	−20.97	−0.12	1.76	−0.11	−6.05	30.9
12	−31.25	−28.07	1.13	−1.01	−0.92	−5.12	13.0
13	−54.15	−54.15	0.93	0.00	0.00	−4.88	4.55

Plate size: L_x = 128 mm, L_y = 128 mm, and L_z = 5 mm; material: GLE-12, clamped, and static load = 1 kN.

Further, using the crack closure integral technique (Buchholz, 1994; Irwin, 1957; Kruger, 2004; Rybicki and Kanninen, 1977) and the nodal force and displacement details, strain energy release rates have been calculated. It may be noted that, as explained earlier, Mode I delamination propagation is not present. It would be predominantly Mode II delamination propagation. Strain energy release rate data for static load of 1 kN have been presented in Table 5 for nodal positions 5, 6, and 7. The delamination propagation takes place when the strain energy release rate at any node exceeds the critical strain energy release rate. As the delamination propagation takes place, i.e. the size of the delamination increases, different models as explained in Table 2 have been used for the study of further delamination propagation. Mode III strain energy release rates at different nodes have also been calculated. It has been observed that these values are very small quantities.

Similarly, studies have been carried out with simply supported boundary condition.

Strain energy release rates with initial delamination size of 4 × 4 mm² at different transverse central static pressure load are presented in Table 6 for clamped boundary condition. Using the fracture criterion, as given in equation (2), the delamination propagation at different nodes has been evaluated. Similarly, studies have been carried out with simply supported boundary condition.

Table 6.

Strain energy release rates at the interface I in a composite plate with a central delamination.

Nodal position	Load 4 kN		Load 5 kN
Nodal position	Model	G_II (J/m²)	Model	G_II (J/m²)
5	1	1744	1	2725
6	1	1403	1	2193
7	1	792	1	1238
5	2	1674	–	–
6	2	1339	–	–
10	3	58	–	–
11	3	442	–	–
10	4	1013
11	4	773
12	4	325
13	4	114

Plate size: L_x = 128 mm, L_y = 128 mm, and L_z = 5 mm; material: GLE-12, clamped, static load, initial delamination size: 2 × 2 mm² for a quarter plate.

Independent experimental studies have been carried out to determine critical strain energy release rates G_I _C (Whitney et al., 1984), G_II _C (Whitney et al., 1984), G_TC (Reeder and Crews, 1990), and G_III _C (Donaldson, 1998). The interlaminar critical strain energy release rates have been obtained along warp direction referred to as 0° direction. Also, the properties have been obtained along 45° direction with respect to warp direction. It was generally observed that the properties are nearly the same along warp and fill directions. The interlaminar critical strain energy release rates for Mode II are presented in Table 7 (Naik et al., 2002b). During the experiments, significant crack growth resistance was observed as the loading was increased. Interlaminar total fracture resistance is also presented for Mode II in Table 7 (Naik et al., 2002b).

Table 7.

Interlaminar critical strain energy release rate and interlaminar total fracture resistance, mode II.

G_IIC (J/m²)		G_IIRC (J/m²)
0°	45°	0°	45°
1343	1168	2648	6469
(±59)	(±11)	(±582)	(±1799)

Material: GLE-12.

With the strain energy release rate presented in Table 6 and the critical strain energy rate values presented in Table 7, delamination propagation studies have been carried out.

At a transverse central pressure load of 4 kN with clamped boundary condition, delamination propagation takes place at nodes 5 and 6 with an initial delamination, as indicated in Model-3. But delamination does not propagate at nodes 7, 10, and 11. The delamination size would be 6 mm along both warp and fill directions for the full plate. With respect to 45° direction, the delamination size would be 5.56 mm for the full plate.

For a load of 5 kN, delamination propagation takes place at nodes 5, 6, and 7 with an initial delamination size of 4 × 4 mm² for the full plate. For the loading conditions considered, delamination propagation just starts around the edge of the initial delamination. The delamination size would be 6 mm along both warp and fill directions for the full plate. With respect to 45° direction, the delamination size would be 8.48 mm for the full plate. A similar observation is made for simply supported boundary condition also.

Experimental studies were carried out on plain weave E-glass/epoxy specimens of 128 × 128 × 5 mm³ dimensions. Artificial delamination of 5 mm diameter was introduced centrally at a distance of 1 mm from the top. There were 5 layers of 0.2 mm thickness above the delaminated interface and 20 layers of 0.2 mm thickness below the delaminated interface. Such specimens are referred to as SP2.

During the experimental studies, on a specimen with an initial delamination size of 5 mm diameter, it was observed that the damage propagation initiated around the initial delamination at 4 kN load.

The central displacements for different models at a load of 1 kN are also presented in Table 2. The results presented in the table are for clamped boundary conditions. As the nodal connectivity is removed at more and more nodes, i.e. as the initial delamination area increases, the central displacement increases.

In-plane damage evolution

During transverse central static pressure loading normal to the plane of the plate, along with delamination propagation, in-plane failure of layers can also take place. In-plane stress state has been evaluated with an initial delamination size of 4 × 4 mm² for the full plate. The in-plane stress state corresponding to static load of 5 kN is presented in Tables 8 and 9 for the clamped boundary condition. Table 8 is for the top surface whereas Table 9 is for the bottom surface. In these tables, the stresses corresponding to different nodal positions are presented. It may be noted that

σ_{x}

is along warp and

σ_{y}

is along fill. Also, it may be noted that

σ_{y}

is greater than

σ_{x}

Table 8.

Nodal in-plane stresses in a composite plate with a central delamination in global co-ordinate system.

Nodal position	Nodal stress (MPa)
	Top surface			1 mm below			0.2 mm below			Average
	σ_x	σ_y	τ_xy	σ_x	σ_y	τ_xy	σ_x	σ_y	τ_xy	σ_x	σ_y	τ_xy
1	−1421	−1421	−1	572	572	−1	−1023	−1023	−1	−1023	−1023	8
2	−1045	−1184	15	163	391	−20	−803	−869	8	−803	−837	35
5	−283	−610	22	−564	14	−27	−339	−485	12	−286	−479	41
10	−49	−364	9	−584	−248	−7	−156	−341	6	−141	−351	18
17	−190	−344	6	−226	−193	0	−198	−314	5	−210	−325	9
26	−199	−313	4	−171	−177	1	−193	−286	3	−202	−298	6
37	−192	−290	3	−143	−165	1	−183	−265	2	−190	−276	4
50	−181	−270	2	−125	−155	1	−170	−247	2	−176	−258	4
65	−167	−253	2	−111	−146	1	−156	−232	2	−162	−241	3
82	−154	−238	2	−100	−138	1	−143	−218	1	−149	−227	3
101	−141	−224	1	−90	−130	1	−131	−205	1	−136	−214	2
122	−128	−211	1	−82	−123	1	−119	−194	1	−124	−202	2

Plate size: L_x = 128 mm, L_y = 128 mm, and L_z = 5 mm. Material: GLE-12, clamped, static load = 5 kN, top surface, initial delamination size: 4 × 4 mm².

Table 9.

Nodal in-plane stresses in a composite plate with a central delamination in global co-ordinate system.

Nodal position	Nodal stress (MPa)
	Bottom surface			1 mm above			0.2 mm above			Average
	σ_x	σ_y	τ_xy	σ_x	σ_y	τ_xy	σ_x	σ_y	τ_xy	σ_x	σ_y	τ_xy
1	439	439	−1	233	233	−1	398	398	−1	410	410	−1
2	426	432	−1	228	229	−1	387	391	−1	402	404	−2
5	394	412	−2	212	219	−2	357	374	−2	372	386	−4
10	348	384	−3	192	206	−2	317	349	−3	330	361	−5
17	300	354	−3	171	193	−2	274	322	−3	286	334	−5
26	257	325	−3	150	179	−2	236	296	−3	246	307	−5
37	221	299	−3	134	168	−2	204	273	−2	213	284	−4
50	193	277	−2	119	157	−2	178	253	−2	186	263	−4
65	171	257	−2	107	148	−1	158	236	−2	166	245	−4
82	154	241	−2	96	139	−1	142	221	−2	148	230	−3
101	139	226	−2	87	132	−1	128	207	−2	134	216	−3
122	126	213	−2	78	124	−1	116	195	−1	121	203	−3

Plate size: L_x = 128 mm, L_y = 128 mm, and L_z = 5 mm; material: GLE-12, clamped, static load = 5 kN, bottom surface, initial delamination size: 4 × 4 mm².

Figure 2 represents identification of nodal positions for the calculation of stresses at a node based on average stress criterion (Nuismer and Whitney, 1975; Whitney and Nuismer, 1974). Nodal positions 1, 2, 3, and 4 can be identified in Figures 1 and 2. These nodal positions refer to the interface region. The element ‘1234abfe’ is in the topmost region. The adjacent element is ‘ijdcghba’. It may be noted that nodes 1 and c as well as 2 and d are the same.

The compressive stress state on the top surface corresponding to the nodal position ‘a’ is calculated based on average stress over one layer thickness of 0.2 mm and over a width of two elements, i.e. 2 mm. In other words, the stress at node ‘a’ is the average of stresses corresponding to nodes a, g, e and points l, k, m. Stresses at points l, k, and m were obtained by intrapolation. Similar approach has been used for calculating the stresses at each node at the center line of the plate along x-direction. It has been observed that the compressive failure would take place up to 10 mm on either side of the center along both warp and fill directions for the clamped boundary conditions at 5 kN static load. Total length of damage would be 20 mm on the top surface for the full plate. These observations are for ultimate failure of the strand under compression.

The nodal positions presented for the top surface in Table 8 are based on considering the nodes as represented in Figure 1(d) are on top surface.

Similar studies have been carried out for the tensile stress state and damage progression on the bottom surface using average stress criterion. The stress at the node $c'$ is the average of stresses corresponding to the nodes/points $c', 4', m', l', k'$ , and $i'$ . It has been observed that the tensile failure would take place up to 8 mm on either side of the center along both warp and fill directions for the clamped boundary conditions at 5 kN static load. Total length of damage would be 16 mm on the bottom surface of the full plate. These observations are for pure matrix block failure under tension.

The nodal positions presented for the bottom surface in Table 9 are based on considering the nodes as represented in Figure 1(d) are on bottom surface.

In-plane damage progression has been studied along other directions also. For the clamped boundary conditions with 5 kN static load, $σ_{x}$ is −299 MPa and $σ_{y}$ is −299 MPa on top surface at node 7. The corresponding average stresses are −290 MPa and −290 MPa, respectively. Total length of damage would be 14.14 on the top surface for the full plate along 45° direction.

For the clamped boundary conditions with 5 kN static load, $σ_{x}$ is 374 MPa and $σ_{y}$ is 374 MPa on bottom surface at node 7. The corresponding average stresses are 338 and 338 MPa, respectively. Total length of damage would be 14.14 mm on the bottom surface for the full plate along 45° direction.

Based on the in-plane average stress state as given in Tables 8 and 9 and the material properties as given in Table 1, the damage area has been predicted and damage dimensions along warp and fill directions and along 45° direction are presented in Table 10. The shape of the damage is quasi-square/quasi-lemniscate.

Table 10.

Damage dimensions (mm) predicted at transverse central static patch loading of 5 kN for specimen SP2a with initial central delamination of 4 × 4 mm².

Type of failure	Boundary conditions	Top surface		Bottom surface
Type of failure	Boundary conditions	Along warp/fill	Along 45°	Along warp/fill	Along 45°
Ultimate failure	Clamped Simply supported	20 40	14.14 28.28	8 20	5.66 15.10
Transverse strand failure	Clamped Simply supported	26 48	19.80 41.58	–	–
Pure matrix block failure	Clamped Simply supported	–	–	16 30	14.14 29.57
Delamination^a	Clamped Simply supported	6 6	8.48 8.48

Delamination at 1 mm below from the top surface.

The experimental results for specimen SP2 are presented in Figure 3 and Table 11 (Naik and Reddy, 2002). Damage dimensions under transverse central quasi-static patch loading are presented in Table 11. Figure 3 presents load–displacement plot for GLE-12, plain weave E-glass/epoxy laminate with central delamination under transverse central quasi-static patch loading with clamped boundary conditions. From Figure 3 and Table 11, it can be seen that the maximum load taken by the laminate is 4.9 kN. Experimental details and damage patterns are presented in brief in Appendix 3.

Table 11.

Damage dimensions (mm) for specimens SP2 under transverse central quasi-static loading: experimental studies.

SP. no.	Load (kN)	Top surface		Bottom surface		Against bright light
SP. no.	Load (kN)	Along warp	Along fill	Along warp	Along fill	Along warp	Along fill	Along 45°
SP2-1	3.0	Just initiated		No damage		No damage
SP2-2	4.0	–	–	8	8	8	8	8
SP2-3	4.9	28 (±2)	25 (±0.5)	28 (±4)	27 (±2)	28 (±4)	27 (±2)	17 (±1)

Figure 4 shows predicted and experimentally obtained damage shapes and sizes superimposed over each other. The experimental results are at the maximum load of 4.9 kN whereas the predictions are at 5 kN.

The predictions are based on both clamped and simply supported boundary conditions. The damage shapes are predicted for pure matrix block failure, transverse strand failure as well as ultimate failure.

For the top surface with compressive stress, damage is primarily due to the strand failure. The experimental studies indicated failure of the strand. The diffused damage because of pure matrix block failure was not clearly seen. Hence, the experiment results match well with those predicted for ultimate failure.

For the bottom surface with tensile stress, damage was observed to be the combination of strand failure and clearly visible matrix cracking. In the outer damaged region of the bottom surface, diffused matrix cracking was present. The experimental results are nearer to those predicted for pure matrix block failure.

During experiments, boundary condition was not exactly clamped. During loading, the composite plate could still slide. Hence, at a transverse load of 4.9 kN, the boundary condition could be in between clamped and simply supported. Lammerant and Verpoest (1996) observed that the specimens could slide during transverse quasi-static patch loading tests.

Comparison of damage sizes and patterns

In-plane damage and delamination dimensions predicted at transverse central static patch loading of 5 kN for specimen SP2a with initial central delamination of 4 × 4 mm² are presented in Table 10. Results are given for both clamped and simply supported boundary conditions. The damage within the layer because of in-plane stresses is more than the damage due to delamination at the interface for the plain weave fabric E-glass/epoxy composite considered.

In these studies, delamination and in-plane failure evolution have been treated independent of each other. The overall damage due to in-plane failure of layers is more significant than the damage obtained due to delamination propagation. This observation is for the material considered, i.e. plain weave fabric E-glass/epoxy composite.

It may be noted that in-plane failure of layers because of in-plane stresses would lead to damage extending to the adjacent interfaces. Even though dalamination propagation at the interfaces obtained independent of in-plane failure of layers is less, the actual value of delamination propagation would be more. Realistically, it would be equal to in-plane damage development because of in-plane stresses within the adjacent layers.

Conclusions

In-plane damage initiation and delamination evolution studies have been carried out on delaminated WF composite plates under transverse static pressure loading, normal to the plane of the plate, distributed over a small area. 3D linear elastic FEA software has been used for the prediction of stress state throughout the composite plate. Possible delamination propagation and initiation of failure of layers because of in-plane stresses have been monitored. Studies have been carried out on a typical plain weave fabric E-glass/epoxy composite plate. Crack closure integral technique has been used for delamination propagation studies. In-plane failure initiation within the layers has been evaluated using maximum stress failure criterion. Based on these studies, the following observations have been made:

The damage evolution takes place both within the layers due to in-plane stresses and at the interfaces due to delamination propagation.

Generally, the damage propagation is more along warp/fill directions than along the other directions. The shape of the damage is quasi-square/quasi-lemniscate.

The damage propagation within the layer because of in-plane stresses is more than the damage due to delamination propagation at the interface for the plain weave fabric E-glass/epoxy composite considered.

Even though delamination propagation at the interfaces obtained independent of in-plane failure of layers is less, the actual value of delamination propagation would be more. Realistically, it would be equal to in-plane damage development because of in-plane stresses within the adjacent layers.

The experimental results match well with those predicted for ultimate failure for the top surface.

The experimental results are nearer to those predicted for pure matrix block failure for the bottom surface.

Funding

This work received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

Footnotes

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