Full-field assessment of the damage process of laminated composite open-hole tensile specimens. Part II: Experimental results

The present paper deals with the investigation of the damage process of glass–epoxy quasi-isotropic laminated open-hole tensile test specimens. The effect of the scaling of ply thickness was also studied, comparing two lay-ups with the same global thickness, with ply-level scaling (PL) [−45₄/90₄/45₄/0₄]_s and sublaminate scaling (SL) [−45/90/45/0]_4s. The grid method was used to provide full-field displacements and strains at the surface of the specimen. It was shown that the cracks could easily be picked up by the method and that it was possible to follow the crack opening as a function of load as the tests proceeded. Moreover, processing the strain maps, it was possible to detect a non-linear behaviour of the material caused by the onset of subsurface cracks in the 90° plies. Finally, the difference between the two lay-ups was underlined. The PL specimens sustained much lower loads to first surface cracking than the SL specimens. It was clearly shown for both specimen types that before the onset of surface cracking, significant subsurface cracking occurred at the hole in the 90° plies. However, because of the higher loads sustained by the SL specimens, subsurface cracking in the 90° plies occurred not only at the hole but also away from the hole.     

Numerical investigation into failure of laminated composite T-piece specimens under tensile loading

This paper presents a rigorous numerical investigation into the structural response of a composite laminate T-piece specimen subjected to a mechanical “pull-off” load case. Initially, a linear elastic stress analysis is conducted, showing very high stresses at the free-edge. In a further analysis, special-purpose interface elements are then inserted where appropriate and used to predict both the crack pattern and the load to failure. It is demonstrated that that using realistic cohesive maximum strength values requires a very fine mesh. Reducing the values to ensure initiation occurs leads to conservative and mesh independent predictions and that a suitable choice leads to good correlation with the experimental results. This study also shows that the T-piece failure is controlled by crack propagation.     

Numerical analysis of size effects on open-hole tensile composite laminates

The tensile strength of open-hole fibre reinforced composite laminates depends on in-plane, thickness and ply lay-up scaling. Translaminar (fibre direction) mode I fracture toughness has recently been experimentally determined to be thickness dependent. This paper presents a computational study of the tensile strength prediction of open-hole laminates using a cohesive zone model. To the authors’ knowledge, it is for the first time in the literature that the thickness-dependence of translaminar fracture toughness is accounted for in the numerical modelling of composites. The thickness size effect in the strength of open-hole composite laminates failed by pull-out is accurately predicted for the first time by a deterministic model. It is found that neglecting delamination in the numerical models will lead to mesh-dependency and over-estimation on the predicted strength. Smeared crack model with cohesive elements to model delamination is able to predict the correct failure mode; but it is found not suitable for accurate strength predictions for laminates failed by delamination.     

Progressive damage assessment of centrally notched composite specimens in fatigue

The aim of this study is to assess the residual properties and the corresponding damage states within centrally notched quasi-isotropic [0/−45/+45/90]_S T650/F584 (Hexcel) carbon-fiber/epoxy composites subjected to fatigue loading using Digital Image Correlation (DIC), radiography, and a non-contact vibration measurement technique. Quasi-static tests were performed on virgin samples using DIC to determine the full-field in-plane strains at different applied load levels. Fatigue tests were interrupted during the fatigue lifetimes in order to perform quasi-static tests with DIC measurements. Non-contact vibration measurements were performed to investigate the effect of fatigue damage on residual frequency responses. X-ray computed tomography was used to determine the type, location, and extent of fatigue damage development. The results provide an important step in the validation of DIC and vibration response as a powerful combined non-destructive evaluation tool for monitoring the development of fatigue damage as well as predicting the damage level of notched composite materials.     

An investigation into the damage development and residual strengths of open-hole specimens in fatigue

An extensive experimental program was carried out to investigate and understand the sequence of damage development throughout the life of open-hole composite laminates loaded in tension–tension fatigue. Quasi-isotropic carbon/epoxy laminates, with stacking sequence [45₂/90₂/−45₂/0₂]_S, [45/90/−45/0]_2S and [45/90/−45/0]_4S were examined. These were selected on the basis that under quasi-static loading the [45₂/90₂/−45₂/0₂]_S configuration exhibited a delamination dominated mode of failure whilst the [45/90/−45/0]_2S and [45/90/−45/0]_4S configurations showed a fibre dominated failure mode, previously described as “pull-out” and “brittle” respectively. Specimens were fatigue loaded to 1 × 10⁶ cycles or catastrophic failure, which ever occurred first. A number of tests were interrupted at various points as the stiffness dropped with increasing cycles, which were inspected using X-ray computed tomography (CT) scanning. A static residual strength program was carried out for run-out specimens of each configuration.     

复合材料开孔层板压缩渐进损伤试验

为研究碳纤维增强树脂基复合材料开孔层板在压缩加载过程中的损伤起始、演化方式和损伤特点,采用微距拍摄、逐级加载超声C扫描、X光扫描和扫描电子显微镜观测4种观测手段对国产CCF300/5228A[45/0/-45/90]4s、[452/02/-452/902]2s、[454/04/-454/904]s3种铺层方式的开孔层板进行了压缩试验研究。对压缩载荷作用下开孔层板的损伤起始和损伤演化进行了观察和对比。对试验中观测到的纤维微屈曲、纤维挤出、孔边开裂和分层扩展等现象之间的关系进行了分析和说明。试验结果表明:压缩载荷下45°和90°铺层相邻位置为层板易分层位置,含45°和90°铺层相邻位置的开孔层板渐进损伤过程较为明显:开孔层板在压缩载荷下较早出现损伤,损伤的起始和演化缓解了孔边应力集中,促使压缩应变能在孔边逐步释放,推迟开孔层板压缩破坏的发生,提高层板压缩承载能力。研究结果可为材料结构损伤容限设计提供依据。     

A simplified approach to the damage tolerance design of asymmetric tapered laminates. Part I: Methodology development

Tapered composite laminates are susceptible to interlaminar damage in the form of delaminations growing from ply drop-off locations. This study presents an analytical method for the calculation of the energy release rates associated with interlaminar cracks emanating from the ply termination in both the laminate thick and thin sections, also accounting for the effects of the tapering angle. The proposed approach is based on modeling asymmetrically tapered composite laminates as assemblies of layered Euler–Bernoulli beam segments; these are split and reconnected through-the-thickness at the ply-drop-off location. The presence of a local resin pocket is explicitly considered in the model. Orthotropic rescaling is employed in order to take into account the material behavior through-the-thickness. This paper presents the analytical formulation of the proposed approach, whose validation follows in part II.     

Impact damage tolerance of laminated composite helicopter blades

The paper is concerned with the study of the damage resistance of laminated composite helicopter blades subjected to impact loading. Dynamic stress intensity factors are determined for composite laminate and separate layers using combined theoretical and experimental approach. The effect of the projectile size on the damage tolerance of composite blade is investigated and tolerable sizes of the defects are estimated.     

Postbuckling of functionally graded fiber reinforced composite laminated cylindrical shells, Part I: Theory and solutions

Buckling and postbuckling behavior are presented for fiber reinforced composite (FRC) laminated cylindrical shells subjected to axial compression or a uniform external pressure in thermal environments. Two kinds of fiber reinforced composite laminated shells, namely, uniformly distributed (UD) and functionally graded (FG) reinforcements, are considered. The governing equations are based on a higher order shear deformation shell theory with von Kármán-type of kinematic non-linearity and including the extension-twist, extension-flexural and flexural-twist couplings. The thermal effects are also included, and the material properties of FRC laminated cylindrical shells are estimated through a micromechanical model and are assumed to be temperature dependent. The non-linear prebuckling deformations and the initial geometric imperfections of the shell are both taken into account. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths of FRC laminated cylindrical shells.     

Low-velocity impact-induced damage of continuous fiber-reinforced composite laminates. Part I. An FEM numerical model

A numerical model for simulating the process of low-velocity impact damage in composite laminates using the finite element method is presented in this paper, i.e. Part I of this two part series on the study of impact. In this model, the 9-node Lagrangian element of the Mindlin plate with consideration of large deformation analysis is employed. To analyze the transient response of the laminated plates, a modified Newmark time integration algorithm previously proposed by the authors is adopted here. We also proved that the impact process between a rigid ball and laminated plates is a stiff system, therefore a kind of A(α) stable method has been advocated here to solve the motion equation of the rigid ball. Furthermore, various types of damages including delamination, matrix cracking and fiber breakage, etc. and their mutual influences are modeled and investigated in detail. To overcome the difficulty of numerical oscillation or instability in the analysis of the dynamic contact problem between delaminated layers using the traditional penalty methods, we have employed dynamic spring constraints to simulate the contact effect, which are added to the numerical model by a kind of continuous penalty function. Moreover, an effective technique to calculate the strain energy release rate based on the Mindlin plate model is proposed, which can attain high precision. Finally, some techniques of adaptive analyses have been realized for improving the computational efficiency. Based on this model, a program has been developed for numerically simulating the damage process of cross-ply fiber-reinforced carbon/epoxy composite laminates under low-velocity impact load. In Part II, this numerical model will be verified by comparing with the experimental results. Also the impact damage will be investigated in detail using this numerical approach.     

Analysis of matrix damage evolution in laminated composite plates

A new model has been developed to investigate matrix cracking in laminated fibrous composite structures. The model can predict matrix cracking and its effect on stiffness reduction. It can also compute the load transfer from the cracked matrix to surrounding fibers. The model is based on the micromechanical concept of the fiber and matrix as well as the matrix material degradation concept as matrix cracking progressed. The micromechanical concept uses a rectangular cell geometry representing a fiber and its surrounding matrix while the material degradation concept uses an empirical expression of a Weibull type function. Two material constants are required for matrix cracking. The constants were obtained from an experiment on matrix cracking. With those constants, the present model predicts the matrix cracking in other cases. The predicted solutions were comparable to the experimental data.     

Similitude study for a laminated cylindrical tube under tensile, torsion, bending, internal and external pressure. Part I: governing equations

A general analytical model is developed for the stresses and displacements of an assembly of several coaxial laminated hollow circular cylinders made of orthotropic layers, and subjected to internal and external pressure, tensile, torsion and bending loads. Slip and friction conditions at the interfaces are not considered in lieu of perfect bonding. The model results are compared to the experimental tensile test of a composite tube. Displacements and stresses are evaluated for different angle-ply layers and radius-tothickness ratios.     

Nonlinear static analysis of composite laminated plates with evolving damage

Considering geometric nonlinearity and damage evolution, the static response characteristics of laminated composite plates subjected to uniformly distributed loading are investigated using finite element approach based on the first-order shear deformation theory. The damage evolution is modeled employing generalized macroscopic continuum theory within the framework of irreversible thermodynamics. The governing nonlinear equations are solved using Newton–Raphson iterative technique. The resulting finite element-based continuum damage model enables to predict the progressive damage and failure load. A detailed parametric study is carried out to investigate the influences of damage evolution, boundary conditions, span-to-thickness ratio, and lamination scheme on the static response of laminated plates undergoing moderately large deformation. It is revealed that the in-plane stretching forces owing to geometric nonlinearity significantly influence the failure load, damage, and stress distribution for immovable thin laminates.     

Effect of hydrogen on the tensile ductility of Ti6Al4V: Part II Fracture of pre-cracked tensile specimens

Pre-cracked compact tensile specimens of Ti6Al4V charged with hydrogen were slowly strained in tension at room temperature and 2.3×10⁻⁵ mm s⁻¹ and a crack-growth monitor used to detect the early stages of slow crack growth and so confirm the load for its initiation. The micro-fractography and crack propagation path were examined by scanning electron microscopy (SEM). The results confirmed that slow cracking preceded fast cracking in all specimens and at hydrogen contents below 90 p.p.m. the stress intensity factor for slow cracking, K_s, increased with increasing hydrogen, whereas it was reduced at higher levels. The average slow crack growth rate increased on increasing the hydrogen content from 10 p.p.m. to 90 p.p.m., but decreased sharply as the hydrogen content was further increased to 125 p.p.m., and then again increased above 125 p.p.m. hydrogen, but only very slowly. With increasing hydrogen content, the slow crack initiation changed from within the α phase to the interface between the α and β phases, the growth path from transgranular to interfacial separation and the fracture mode from the mixed ductile and cleavage to fracture along the α–β interface (≥500 p.p.m.). It is suggested that the mechanism of slow crack growth is different for the different ranges of hydrogen content: at the low hydrogen levels (<90 p.p.m.) the dominant mechanism is creep-induced slow crack growth, whereas the slow cracking becomes controlled by hydrogen diffusion in both α and β phases when the hydrogen content is above 90 p.p.m. Fast fracture was invariably preceded by slow crack growth at all hydrogen levels up to 500 p.p.m. This revised version was published online in November 2006 with corrections to the Cover Date.     

Vibration analysis of laminated composite plates with damage using the perturbation method

The present work focuses on vibration characteristics of damaged laminated composite plates. Damage is considered as a local reduction of anisotropic plate stiffness, and three damage factors (representing the damage severity, damage anisotropy, and damage location/area, respectively) are defined to describe damage status in the laminated composite plates. The analytical solutions are obtained by the perturbation method. A numerical analysis is conducted on the vibration of damaged laminated composited plates, and the effect of damage factors on the vibration characteristics is discussed. Results indicate that three damage factors have different influences on the vibration characteristics. Also, the modal curvatures and strain energy show higher damage sensitivity than the natural frequencies and displacement mode shapes. The perturbation-based vibration analysis developed in this study can be used to effectively evaluate the effect of damage on the vibration behavior of anisotropic plates and potentially identify the damage in the laminated plates.     

Criterion of geometric instability for the process of tensile deformation of thin specimens

Deformation of a long thin rod of uniform cross section is investigated. The problem of geometric loss of strength is considered more rigorously: a deformation equation is derived which describes tension at a constant rate for long and thin specimens in which a possible dependence of cross section on time and coordinates along the specimen axis is taken into account. An instability criterion is established for solving this problem in relation to local variation of the cross section. This criterion of geometric instability is compared with experimental data obtained in studying low-temperature spasmodic deformation.Translated from Problemy Prochnosti, No. 3, pp. 58–62, March, 1991.     

Evaluation of impact assessment methodologies. Part I: Applied methods

The present paper is the first part of a comparative evaluation of two methodologies for the analysis of damage in composites. The subject of the investigation is low-velocity impact and residual compression strength of monolithic composite panels. One of the methodologies is implemented in the tool CODAC, which is a stand-alone software that aims to be a fast tool and works with specialized finite element (FE) and material models. The other methodology IDAT parametrically generates the FE models by using MSC.Patran and performs the analysis by the FE code ABAQUS/Standard. The evaluation in regard to accuracy and efficiency is performed by comparing and judging the models and techniques, which are applied for stress analysis, failure detection, material degradation and time integration. Part I of the paper describes the applied methodologies. In Part II, the methodologies are validated by comparing computational results against experimental results.