This paper presents the thermo-elastic effect on materials having anisotropic behavior and stresses developed due to residual temperature on interlaminar delamination fracture characteristics of composite skin stiffener. For the preexisting interlaminar delaminations subjected to uniaxial loading and three-point bending of three-dimensional coupled field thermo-elastic finite element analyses have been accomplished. The individual mode of strain energy release rate along the delamination front has been evaluated by modified crack-closure integral method based on the concept of mechanics of linear elastic fracture. Qualitative comparison has been illustrated for the individual modes of energy release rate along the delamination front of skin stiffener for both the loadings. The influence of coupled field thermo-elastic material anisotropy of the constituting laminae has been reasoned for the asymmetric variation of total strain energy release rate along delamination front. This was found to be significantly higher for the case of residual thermal stresses compared to mechanical loading.

Composite skin stiffener is being predominantly used as aerospace structures due to their incomparable strength and stiffness ratio. It is also ease of repair and assembly under in-situ loading conditions. However, these composite structures are susceptible to interfacial or interlaminar damage mechanisms such as delamination, debonding or such other involvement like matrix crack and fiber breakage due to defects or flaws arising even during the stage of manufacturing. This problem can also be raised at time of service or maintenance provided to damages, or loss of low-velocity impact or from operative malfunctioning. Among all these damage mechanisms, delamination mode of failure is being considered as most critical failure mechanism because generally, they are embedded in the structure and not visible from outside, and their initial size are very small even for detection by traditional non-destructive testing methodology. Apart from this, during curing stages of multiply stiffeners, residual thermal stresses are induced because of the asymmetric thermal expansion coefficients between differently oriented layers even when the skin-stiffeners are free from any mechanical loading. Initial prediction of the location and size of such delaminations are almost impossible leading to such unpredictability in failure behavior of aerospace and avionics structures made up of composite stiffened panels. Anisotropy of thermoelastic properties and mismatch of expansion coefficients might be coupled detrimental phenomena, which can induce all of a sudden a very small interlaminar damage to promptly evolve and propagate to catastrophic structure failure, especially under the severity of tensile and bending loading conditions during its structural application. Rice [1] reexamined the elastic fracture mechanics concepts for a crack on the interface between different solids. Also, the function theory has been stated in the form of stress and displacement fields at the vicinity of the crack tip. Many authors have investigated the debonding mechanism and damage propagation of skin/stiffener panels and failure analysis applying shell models [2–4] without consideration of manufacturing stage stresses such as thermal residual stresses. These studies focused on the development of step-wise approach to recognize the computational stress investigation and failure mechanism to find the position of first computational failure and matrix cracking to inquire the delamination growth with the use of numerical and experimental testing activities.

In aerospace application, nuclear reactors and chemical plants, the panels/plates composed of polymer based fiber reinforced composite materials during their operational life are generally subjected to hostile environment conditions. Further to the mechanical loading, these structures are regularly subjected to hygroscopic along with destabilizing thermal loading. Lekhnitskii [5,6] developed the solution of two-dimensional linear anisotropic elasticity problems taking complex variable. Also, Amartsumyan [7] illustrated the fundamental theory and equations based on the anisotropic laminar shell. According to the theory of thermo elasticity, there are basically three reasons of the occurrence of thermal stresses: first, if the specimen undergoes by non-uniform temperature field, then second reason is that if the displacements are blocked as the constraints placed on the boundary even with a uniform temperature, and finally, if the materials shows anisotropy, even with uniform heating [8]. As composite materials have layer-wise inhomogeneity behavior, thermal stresses frequently come at interfaces between layers with different coefficients of thermal expansion and dissimilar fiber orientation and, causing distortion and elongating of normal to mid-surface. Due to inter-laminar stresses, critical warping and elongating of cross-section may occur which results in delamination of layers, debonding of matrix or fiber fraction. So, precise prediction of stress and thermally induced deflection becomes important for the investigation of laminate composite in thermal environment. Hahn and Pagano [9] determined the remedial stresses in resin matrix composites laminates for a large range of temperature for different elastic moduli. Author determined the relations between stress, strain and temperature and applied for calculating the curing stresses in epoxy/boron composite laminates.

Usually Classical Laminated Plate Theory (CLPT), First-order Shear Deformation Theory (FSDT) and Higher-order Shear Deformation Theory (HSDT) have been applied as solution of thermal problems in three dimensional theories of composites to minimize computational cost, and to reach appropriate exactness in the field of application. Earlier many authors studied stresses and thermal deformation in symmetric and anti-symmetric laminates using CLPT and FSDT. Ninth order theory has been proposed by Matsunaga [10,11] for sandwiched plates and laminated composites to study the thermal behaviors. Kant and Shiyekar [12] estimated the thermal stresses by using higher order theory for laminated composite plates. Zenkour [13] used Global higher order theory for cross-ply laminated plates to found the analytical solutions.

During last decades, the delamination phenomena of complex composite structures like stiffened composite panels become the prime area of research activities. Many researchers [14–17] have performed experimental activities and numerical investigation on stiffened composite panels containing delamination to enquire the effect of delamination size, depth and position on the panel compressive behavior. Kuriakose and Talreja [18] presented the analytical solutions using variational approach for stresses in two different [90m/0n]s and [0m/90n]s cross-ply laminates with matrix cracks in the 90° layers which is exposed to bending. Suemasu et al. [19] established the numerical advanced models, based on the Virtual Crack Closure Technique (VCCT) and approach of fail release in stiffened composite panels for the simulation of delamination growth and used this numerical analysis of the debonding across stringer and skin. Pietropaoli and Riccio [20] demonstrated that the delamination growth prediction and attained some numerical models, are mostly depend on the finite element size at the delamination front and on the load step size which can be properly set with the aid of a large extent of experimental records. Krueger et al. [21] inspected the debonding behavior for the specimen of skin-stiffener subjected to tension and three-point bending under mechanical loading. In this paper, release rate of total energy and mixed mode ratio have been assessed by using VCCT technique. In other paper [22], authors studied stringer/skin separation of an epoxy/graphite composite panel subjected to shear loading that causes the panel to buckle and resulting out-of-plane deformation. Cetkovic [23] analyzed the thermo-mechanical bending of different materials such as sandwich plates and laminated composite which are subjected to mechanical load as well as linearly variable through the thickness temperature field. A MATLAB program has been used to measure the impact on geometry of plate and change of material orthotropy. In other paper, Springer and Tsai [24] analyzed thermal conductivity of unidirectional composites and derived an expression for calculating these conductivities in both the directions i.e. along and normal to the filaments. Also, thermal expansion coefficient of the composite has been analyzed and calculated by the method of energy principles. Riccio et al. [25] applied the approach VCCT for the numerical investigation of skin-stringer debonding growth under compressive load in stiffened panel of composites. Three-dimensional thermo-elastic analysis of the composite under residual thermal stresses has been performed for the determination of fracture mechanism of imperfect interfaces and cracks [26,27].

Large number of literatures is accessible on delamination of composites owing to mechanical loading and very few are related to the phenomena of thermo-mechanical impact and ply orientation on fracture behavior of embedded delaminations. Due to the change in temperature range from 70 °C (room temperature) to 180°C (fabrication temperature), thermal stresses produced cannot be ignored during manufacturing of polymeric composites laminates. So, it is logical in composite materials that the inter-laminar damage depends on both the mechanical loading and residual stresses. This damage behavior of embedded delamination structures is significantly affected by these residual stresses and so it should not be neglected during failure analysis.

The main objective of this research work is to explore the thermo elastic effect on the fracture of FRP composite laminates undergoing bending and tensile loading using fracture mechanics approach. Interlaminar fracture energy has been analyzed to delamination front and demonstrates the growth of delamination crack. Also, for evaluating the influence of crack front on the behavior of thermo-elastic fracture, an analysis of superposition has been performed.

2Computation of energy release rateLinear Elastic Fracture Mechanics (LEFM) is helpful for composite laminates to describe the growth of delamination [28]. In fracture mechanics, the strain energy release rate (SERR), GT, is evaluated along the delamination front and is consists of three different components. These three components emerges due to different reasons as first component, GI, emerges because of inter-laminar tension, on the other hand, second component, GII, emerges due to inter-laminar sliding shear and the reason of third component, GIII, arises is to inter-laminar scissoring shear. These above components are then compared to the values of inter-laminar fracture toughness to evaluate the delamination progress. These values are enumerated experimentally under mixed mode loading, i.e, mode I and II loading [29–31]. Modified Crack Closure Integral (MCCI) methods applied to determine all the modes of SERR [32,33] as shown in Fig. 1. To study the damage phenomena of composite laminates, an analysis of three dimensional finite element has been applied. The present study focused on the effect of thermo-elastic residual stress on the mixed-mode delamination crack growth behavior due to thermal and mechanical loading.

The components of strain energy release rate at each and every point is obtained by superposing their respective effects on the delamination front under mechanical and thermal loading due to uniform temperature drop from curing temperature to room temperature, based on assumptions of linear elasticity [34]. By the propagation of a crack of length ‘a’ to ‘a+Δa’, the energy released can be expressed as

Where, the subscripts M and T denote mechanical and thermal loading respectively. Δ (x-Δa) term represent the crack opening displacement from the top to bottom delaminated surfaces and σ (x) signify the stress at the crack front required to close the delaminated area. The three different components of strain energy release rates for mode I, II and III can be shown as:Now, total energy release rate G can be determined by considering the algebraic sum of the individual modes and expressed as follow

σzz τzx τzy are the interlaminar stress and δuz, δux, δuy are relative opening, sliding and tearing displacements respectively of the initial delaminated surfaces.

The skin/stringer specimen is subjected to tension and three-point bending load, separately. First set of finite element interlaminar fracture analysis is executed for a purely mechanical loading. Also, the analysis has been done for bending load. The strain energy release rate has been computed separately for two different loading.

Then another analysis has performed, where the laminate has subjected to only thermal loading because of uniform temperature drop from the curing temperature to room temperature. The values of displacements and stresses thus obtained have superposed with the results attained from uniaxial tensile loading for calculating the components of strain energy release rates due to the thermal, mechanical and superposition of these two loadings. Then strain energy release rate around the delamination front has evaluated and expressed in following equation. The values of individual components of strain energy release rate have been substituted from Eq. (2) in Eq. (3).

Now the expression derived has been stated next by separating and rearranging the terms w.r.t. individual parameters M, T and their interactions respectively.

After re-shuffling the similar subscripted terms, the expression for G as follow

where,where GM, GMT, GT represents the different strain energy release rate components due to mechanical, superposition of individual effects thermo-mechanical loading and only thermal loading respectively.3Finite element modelingA skin-stiffener debonded specimen with lay-up sequence has been considered for analysis. The specimen consists of a bonded skin and flange assembly as demonstrated in Fig. 2. An epoxy/graphite system has been used for both skin and flange. The skin is made up of a tape with defined average ply thickness of h=0.148mm and has a [45/−45/0/−45/45/90/90/−45/45/0/45/−45] lay-up. The flange has developed with plain-weave fabric taking thickness of h=0.212mm. The flange lay-up has [45/0/45/0/45/0/45/0/45]f, where the “f” represents fabric, “0” denotes a 0°–90° fabric ply and “45” signifies a 0°–90° fabric ply rotated with an angle of 45°. Taking the specimen length has 101.6mm and width 25.4mm.

In the present study, layered 3D solid elements have been applied to model. The complete analysis domain and the characteristics of delamination were simulated with the help of multi-point constraints along the delaminated interface. The interface resin layer, having delamination pre-existing, has the properties of a low modulus isotropic material. Adhesive has been used as the interface layer between skin and flange. The interlayer has exhibited as two separate layers, having same isotropic properties, placed above and below the delamination plane. Angles of fiber were measured counter-clockwise from the x-axis. Inside the delamination zone compatible contact/gap elements were used to avoid the interpenetration of both top and bottom layer, which otherwise would responsible for physically unrealistic analysis. Advanced propagation of delamination front has been recognized by carefully removing the constraints along the interface of adjacent sub laminates.

The skin or stringer sample has subjected to three-point bending load and tension. Firstly, finite element inter laminar fracture investigation has implemented only for a mechanical loading in the form of tensile as well as bending loads. In case of tensile loading, 17.8kN has been applied at the tape skin right edge in the x-direction while for bending load, 427.8N has been applied in y-direction at the middle lower portion of tape skin. The second set is thermo elastic fracture behavior in which mechanical loading has applied to the uniform temperature drop from stress free state at 160°C to room temperature 30°C to induce thermal residual stresses in the laminate. In the third set of analysis, only thermal residual stresses have been applied through uniform temperature drop.

With the help of ANSYS software, stress has been calculated all over the composite laminate using finite element analysis. For further analysis, eight nodes of that element (Solid 185) has generated with three degrees of freedom (translations in the X, Y and Z directions). The orthotropic thermo-elastic material properties of the epoxy/graphite material and the adhesive have summarized and shown in Table 1.

Thermoelastic material properties [35,36].

Unidirectional prepreg | Plain wave fabric | Adhesive | |
---|---|---|---|

Elastic properties | |||

E11 (GPa) | 161.0 | 71.7 | E=1.72 (GPa) |

E22 (GPa) | 11.38 | 71.7 | |

E33 (GPa) | 11.38 | 10.3 | |

G12 (GPa) | 5.17 | 4.48 | G=1.42 (GPa) |

G13 (GPa) | 5.17 | 4.14 | |

G23 (GPa) | 3.92 | 4.14 | |

υ12 | 0.32 | 0.04 | υ=0.3 |

υ13 | 0.32 | 0.35 | |

υ23 | 0.45 | 0.35 | |

Thermal properties | |||

αx (/0C) | 0.025×10−6 | 0.02×10−6 | α=44×10−6 (/oC) |

αy (/0C) | 0.025×10−6 | 0.02×10−6 | |

αz (/0C) | 22.5×10−6 | 19.5×10−6 | |

Temperature State: | |||

Curing temperature=160°C | |||

Room temperature=30°C | |||

ΔT=−130°C |

Under the application of loading and boundary conditions, the flange gets debonded from the skin. The enlarged view which has developed by finite element (FE) model of interface delamination for studying the thermo-elastic effect on fracture crack growth behavior for the multi-layered epoxy/graphite laminate sample as shown in Fig. 3. It can be illustrated from figure that refined meshing has been done at the critical zone, where the crack is detected during the test. Stresses and displacements were obtained from three dimensional finite element (FE) analysis. With the significant variation of temperature from curing temperature to room temperature, both properties (thermo-elastic and mechanical) were supposed to remain constant.

4Results and discussionStrain energy release rates are generally evaluated for non-linear finite element analysis at front location of applied loads. Whereas, in foregoing analysis, the results were computed across the width of the specimen, i.e., at x=62.23mm. A three dimensional thermo-elastic FE analysis has done to check the possibility of bending-stretching coupling because of thermo-mechanical loading on laminated sample for bending and tensile loading. Three modes of strain energy release rates i.e. Mode I, II and III mainly spread over a zone of delamination front. The uneven distributions have found to be different for many types of loading. Moreover, the total energy release rate G=GI+GII+GIII, along the center line of the sample has found from 3D analysis. Different modes of strain energy release rate along the delamination front for all different loading situation on laminated composite have been discusses below.

4.1Three-point bending loadFigs. 4–6 illustrate the delamination crack growth behavior of different modes of strain energy release rate distribution. The delamination crack growth behavior have been accomplished and strain energy release rate along delamination front were calculated from stresses and displacement found from three-dimensional thermo-elastic investigation. The distribution is non-uniform along the length, i.e., from z=0 to 25.4mm. The comparison is done between the values of GI,GII,GIII and width of sample when skin stiffener is subjected to mechanical and thermo-mechanical loading under three-point bending. Fig. 4 presents the variation of GI for different values of width of the specimen. It has been observed that SERR value for two different loadings are different. Value of GI is dominant for thermo-mechanical except some places where it is higher for mechanical loading.

Fig. 5 demonstrates that SERR value for both types of loading is approximately same. The similarity in the energy release rate value is due to the less effect of thermal residual stress on interlaminar sliding shear. Referring SERR to the mode III, there is large variation in the values of energy for both stresses (Fig. 6). There is very less variation in the value of GIII for thermo-mechanical loading. Referring SERR to the mechanical loading, the energy release rate attains very high value and the maximum is 1.025J/m2. The domination of fracture rate in case of thermo-mechanical is due to the thermal residual stresses. The asymmetry in the values of GIII is higher for the thermo-mechanical coupled field comparing to mechanical loading applied alone. For all loadings, the initial energy value is low and then it increases.

4.2Tensile loadFigs. 7–9 show the deviation of energy release rate w.r.t width around the delamination front for epoxy laminate under tensile loading. The analysis has performed for drop of temperature uniformly and successive tensile loading on the pre-stresses laminate. Similar to the bending load, here also SERR fluctuates rapidly for mechanical and thermo-mechanical loading. Fig. 7 shows inter-laminar fracture energy release rate (Mode I) as a factor of distribution w.r.t different width position over the delamination zone. Maximum energy value is 450J/m2 at z=14mm along delamination front for the thermo-mechanical loading indicating severity of delamination propagation at this point. Similar to the bending, GII has nearly same value for both mechanical and thermo-mechanical (Fig. 8). Maximum GII occurs at the middle part of width and then gradually decreases.

The variations of mode III with respect to z-axis have been described in Fig. 9, considering the mechanical loading and thermal residual stresses. Figures revealed that initial values of GIII is approximately same for both loadings. The significant difference between GIII values along the delamination front shows inter-laminar residual stresses, which was developed due to initial thermal loading on laminated sample. Near the edges of sample, energy release rate attains lowest value for mechanical load and at the center it has higher value. Similar difference has been observed for thermo-mechanical, but the energy value is higher compared to former.

Fig. 10 shows the variation and dominance of the total SERR under the coupled effect of thermal and mechanical loading along the delamination front for both tensile and bending loads. According to the figure, there is a mismatch in EER along the delamination front for both mechanical and thermo-mechanical. The maximum G occurs at z=25mm for thermo-mechanical loading. More over along the width, the fracture energy possesses lower value for thermal in comparison to thermo-mechanical and mechanical loading. Due to thermal residual stresses, there has significant difference in energy for the interval from 0 to 25.4mm width position of delamination front. It is also comprehended from the figure that total energy release rate is more in case of bending load in comparison to tensile load.

SSERR values unevenly distributed due to transition of thermo-elastic stress field along the delamination front. The multiple peaks in SERR plots at several locations similar a monolithic cracked structural component.

It can be noted from energy release rate analysis of tensile and three point bend loads that it magnifies the mixed-mode inter-laminar delamination crack growth due to the coupling effect of thermal residual stresses, on the other hand, it also disagrees the interface crack growth mechanism subjected to the location of embedded delamination front. The variation of SSERR in composite laminates describes the physical mechanism responsible for constrained delamination propagation. At most of the peaks, effects become more affirmed, either reducing or increasing the energy release rate for individual modes.

5ConclusionsIn 3-dimensional thermo-elastic analysis, modeling and simulation of interlaminar delaminations have conducted for FRP composite laminates subjected to bending and tensile loading. Study of material properties and thermal residual stresses on progressive delamination front propagation have been carried out. Strain energy release rate procedure has been implemented to analyze the thermo-elastic fracture behavior of the interlaminar delamination. Due to the constraining effect of the thermal residual stresses and the interaction of the thermo-elastic stress field, it has been found that energy release rate plots exhibit unsymmetrical variation w.r.t. the width of the sample along the delamination front. Following conclusions were drawn from the analysis of delamination behavior in the composite material due to residual stresses.

- 1
In a multi-lay up laminate, the thermo-elastic properties placed a re-straining effect at the interface on the adjacent plies. The residual thermal stresses developed might be retarded or extended the mechanism of delamination evolution subjected upon the type of loading.

- 2
Strain energy rate plots found were unsymmetrical with and without taking the thermo-elastic superposed effect of residual stresses due to the anisotropy ratio of thermal expansion.

- 3
First mode of energy release rate was the main leading component of the total energy release rate and plays a significant role in characterizing the delamination crack growth behavior and failure of composite laminates for both three point bending and tensile loading.

This work shows the relative influence of residual thermal stresses and loading condition on the delamination propagation behavior in FRP laminates and consequently should be taken into account in damage development studies.

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