Numerical Modeling of Combined Matrix Cracking and Delamination in Composite Laminates Using Cohesive Elements

Sub-laminate damage in the form of matrix cracking and delamination was simulated by using interface cohesive elements in the finite element (FE) software ABAQUS. Interface cohesive elements were inserted parallel to the fiber orientation in the transverse ply with equal spacing (matrix cracking) and between the interfaces (delamination). Matrix cracking initiation in the cohesive elements was based on stress traction separation laws and propagated under mixed-mode loading. We expanded the work of Shi et al. (Appl. Compos. Mater. 21, 57–70 2014) to include delamination and simulated additional [45/?45/0/90]_s and [0₂/90_n]_s {n?=?1,2,3} CFRP laminates and a [0/90₃]_s GFRP laminate. Delamination damage was quantified numerically in terms of damage dissipative energy. We observed that transverse matrix cracks can propagate to the ply interface and initiate delamination. We also observed for [0/90_n/0] laminates that as the number of 90° ply increases past n?=?2, the crack density decreases. The predicted crack density evolution compared well with experimental results and the equivalent constraint model (ECM) theory. Empirical relationships were established between crack density and applied stress by linear curve fitting. The reduction of laminate elastic modulus due to cracking was also computed numerically and it is in accordance with reported experimental measurements.     

Tensile Behaviour of Multilayer Knitted Fabric Composites with Different Stacking Configuration

In this paper, multilayer plain weft knitted glass fabric reinforced epoxy composite laminates with different stacking configurations, i.e., [0°]₄, [0°/±45°/0°], [0°/90°/90°/0°] and [90°]₄, were investigated experimentally. The laminates were uniaxially tensile loaded until final fractures occurred. The experimental results show that with the change in layer stacking structure, a corresponding variation in composite strength and stiffness was achieved. The tensile strength and modulus rank as follows: [0°]₄ > [0°/±45°/0°] > [0°/90°/90°/0°] > [90°]₄, which implicates a potential desiguability of Knitted Fabric Composites (KFC) for engineering applications. Failure behaviours of the fractured laminate specimens were examined using a matrix digestion and layer peeling method, based on which the behaviour of each lamina in the laminate can be clearly shown. It was found that an angle-plied lamina in the laminate when subjected to a uniaxial tensile load has a different fracture mode from that of a single ply composite under an off-axial tensile load. This means that the lamina in the laminate is subjected to a more complicated load combination. By comparing the fractured mode of the latter lamina with that of the single ply composite, the load direction sustained by the lamina in the laminate can be identified, which provides a qualitative benchmark for verifying a theoretical simulation.     

Failure behavior of quasi-isotropic carbon fiber-reinforced polyamide composites under tension

In this paper, the microscopic failure behavior of quasi-isotropic carbon fiber-reinforced polyamide-6 (CF/PA6) laminates under tension was investigated experimentally. Laminates of two layups, namely [45°/0°/?45°/ 90°]_s and [45°/0°/?45°/ 90°]_2s, were made from CF/PA6 tapes of two different manufacturers and then subjected to tensile testing. Crack initiation and progression on the polished free edge of specimens were examined using optical microscopy, under several load levels. Crack growth behavior through the specimen width was also traced by observing the crack configurations in different sections in the specimen width direction. The effects of the spatial distribution of fiber on the microscopic damage events were elucidated. The difference in failure behavior between the present CF/PA6 laminates and conventional thermosetting CF/Epoxy laminate is discussed.     

Simulation of discrete damage in composite Overheight Compact Tension specimens

Damage progression in laminated Overheight Compact Tension specimens was modeled using discrete representations of individual cracks and delaminations. Matrix cracking and delamination initiation, propagation, and interaction, without any prior knowledge and/or meshing of matrix cracking surfaces, is accomplished by combining stress and fracture mechanics-based constitutive modeling within a mesh independent crack-modeling framework. Simulation results including only matrix damage for specimens with [45₂/90₂/?45₂/0₂]_s and [0₄/90₄]_2s stacking sequences were compared with load–displacement curves and 3D X-ray micro computed tomography results from tested specimens. Excellent correlation was shown between the simulated and experimental load–displacement curves including statistical variations and proper representation of both the curve non-linearity and peak load. Similarly, a high level of correlation between simulated and experimental damage extent was shown. Additionally, a [45/90/?45/0]_2s specimen exhibiting significant fiber fracture was modeled and results compared with experiment. Fiber fracture was simulated using a continuum damage mechanics approach in addition to the discrete cracking and delamination damage representations of matrix damage. The simulated load displacement curve and damage extent compared favorably with experimental results.     

Fatigue life estimation of graphite/epoxy laminates under consideration of delamination growth

A closed form approach to the assessment of the fatigue life of graphite/epoxy laminates under cyclic tension–compression loading has been developed. The model is mechanistic and uses cyclic energy release rates for prediction of delamination growth and of critical delamination sizes which induce buckling and the final failure of the laminates. Tests performed with graphite/epoxy specimens of stacking order [0_n, ?_m]_s with severed central plies [?], and of stacking order [0₂, +45, 0₂, ?45, 0, 90]_s with a central unloaded hole, indicate good correlation between estimated values and observed delamination growth, critical buckling strength of separated plies and load cycles to failure.     

An Investigation of the Effects of Layer Architecture on Tensile Damage Mechanisms in a Silicon Carbide (SiC) Fiber-Reinforced Titanium Matrix Composite

This paper presents the results of recent studies of the effects of layer architecture (±45° and 0/±45°) on deformation and cracking phenomena in Ti-15-3/SCS-6 (SiC) composites. Deformation and cracking phenomena were elucidated by microscopic observations during incremental loading to failure. The initial damage occurred early via debonding between the fibers and the predominantly TiC reaction layer. This was followed by a complex sequence of damage that included: matrix cracking, sub-grain formation, stress-induced alpha phase precipitation, microvoid nucleation and coalescence, fiber fracture and catastrophic failure. Fracture in the [±45°]_2s composite occurred by shear mechanisms. However, an axial failure mode was observed in the [0±45°_2s composite. The composite strengths are compared with empirical estimates obtained from the Tsai–Hill criterion.     

Simulation of fatigue performance of cross-ply composite laminates

The fatigue life of cross-ply composite laminates was evaluated using a statistical model. A modified shear-lag analysis was applied to describe the cycle-number-dependent stiffness reduction and consequent stress redistribution processes in the laminates resulted from both progressive transverse matrix cracking in transverse plies and local delamination at tips of transverse cracks. From the strength degradation behaviour and the static strength distribution of 0° plies as well as the fatigue behaviour of 90° plies, the fatigue life of cross-ply laminates with various types of lay-up can be simulated from the model. Predictions of fatigue performance are compared with experimental data for [0/90₂] _s , [02/90₂] _s and [0₂/90₄] _s graphite/epoxy cross-ply laminates: good agreements are obtained.     

Waveguide IMPATT diode oscillators with cap structure

Abstract

An experimental study of the mechanical properties of graphite/glass/graphite interply hybrid composite laminates subjected to pure tension and pure flexure is reported. The investigation includes single‐graphite, single‐glass and hybrid composite laminates. Straight side test coupons with dimensions of 200 mm × 14 mm and various numbers of layers were fabricated by hand lay‐up molding method. Epoxy resin served as the base matrix material. The types of layup of fabric warp directions include: 0°, 45°, 90°, [0°₃/45°/0°₃] and [0°₃/45°/45°₃].

Emphasis is given to the studying of the strength‐deformation behavior and the associated crack patterns of hybrid composite laminates, for monotonically‐increasing logitudinal elongation and angular deflection. Stress‐strain characteristics and crack patterns distinctive to each type of the specimen tested are presented. Mechanical strength data for hybrid composite laminates indicate the improvement in material characteristics over the single‐graphite fabric laminates.     

Experimental study of damage characteristics of carbon woven fabric/epoxy laminates subjected to lightning strike

This paper experimentally investigates the damage characteristics of two stacking sequenced ([45₂/0₂/−45₂/90₂]s, [30₂/0₂/−30₂/90₂]s) carbon woven fabric/epoxy laminates subjected to simulated lightning strike. Characteristics of the damage are analyzed using visual inspection, image processing, ultrasonic scanning and scanning electron microscope. The mechanical properties of post-lightning specimens are then studied. Observations show that as the lightning strike is intensified, an enlarged resin pyrolized area appears majorly along the weft orientation while the delamination region extends equally to both of the warp and the weft direction. The resin/fiber interfacial bonding is severely damaged by a thermal–mechanical effect due to lightning strike infliction. Mechanical testing further shows that the stacking sequence can influence the failure significantly. Compared with prepreg taped material, the restrained damage area due to special designed stacking sequence, lamina thickness and the weft nylon binder make the woven fabric reinforcement a good choice for the fabrication of lightning protection structures.     

Modelling delamination onset and growth in pin loaded composite laminates

A three-dimensional (3D) finite element (FE) model is created with cohesive zone elements (CZE) to simulate a mechanically fastened [0°/90°]_s pin-loaded joint in a composite laminate. The model incorporates fully integrated solid elements in the pin-loaded area to accurately capture the high stress gradients. Contact based cohesive elements with a bilinear traction–separation law are inserted between the layers to capture the onset and growth of delamination. The stress distribution around the pin-loaded hole was verified with the widely used cosine stress distribution model. Results from the FE model show that delamination damage initiated at the point of maximum average shear stress at the 0°/90° interface. The delaminated area develops an elliptical shape which grows in a non-self similar manner with increasing pin displacement. It is concluded that a progressive damage model should be included to provide a full understanding of the failure sequence, work that the authors are currently engaged with.     

The tensile behavior of a silicon carbide fiber-reinforced titanium matrix composite

This paper summarizes the results of a study on the effects of composite microstructure and test temperature on tensile deformation and fracture behavior of a symmetric [0/90]_2s titanium alloy metal-matrix composite. Matrix microstructure is controlled by heat treatment, which is used to produce metastable or Widmanstatten + microstructures. The sequence of damage initiation and evolution at both room and elevated temperature (650°C) is identified using ex-situ scanning electron microscopy observations during incremental monotonic loading to failure. The nature, sequence and complexity of damage during uniaxial loading is presented and discussed in light of competing and mutually interactive influences of load level and deformation characteristics of the microstructure.     

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。     

Mode II Interlaminar Fracture of Filament Wound Angle-ply Specimens

This paper presents a study of the interlaminar fracture of filament wound composites. Mode II end notched flexure (ENF) tests were performed on flat glass/polyester specimens. The tested specimens had asymmetric [±]₄ angle-ply stacking-sequences, with values from 0.8° (hoop winding) to 30°. Due to the low stiffness and probable high toughness, it was not possible to propagate the crack in [±60°]₄ specimens before they suffered considerable permanent deformations. A short support span had to be employed for [±30°]₄ specimens in order to obtain crack propagation. Nevertheless, the results for those specimens should be viewed with caution, as some nonlinear behaviour and small permanent deformations were detected. No other unusual features, such as crack jumping to other interface, were observed. The scatter in the critical strain energy release rate values (G _IIc ) was higher for [±10°]₄ and [±30°]₄ specimens than for the quasi-unidirectional ones. G _IIc values from the insert were generally lower than those from mode II pre-cracks, except for quasi-unidirectional specimens. A plot of average G _IIc values against showed a minimum at =5°.     

Damage response of stitched cross-ply laminates under impact loadings

The impact response of stitched graphite/epoxy laminates was examined with the aim of evaluating the efficiency of stitching as a reinforcing mechanism able to improve the delamination resistance of laminates. The investigation, which focussed on two classes of cross-ply stacking sequences ([0₃/90₃]_s and [0/90]_3s), showed that the role of stitches in controlling damage progression of laminates and their capability to reduce the impact sensitivity of specimens are greatly dependent on the impact behaviour of base (unstitched) laminates. In [0₃/90₃]_s laminates, in particular, stitching is able to reduce damage area, on condition that the impact energy is higher than a threshold level and delaminations are sufficiently developed. In [0/90]_3s laminates, on the other hand, stress concentration regions generated by the stitching process appear to promote the initiation and propagation of fibre fractures, thereby inducing a decrease in the penetration resistance of the laminate.     

Time-dependent micromechanical behavior in graphite/epoxy composites under constant load at elevated temperatures

Time dependent deformation at the individual fiber level was investigated in graphite fiber/epoxy composites at elevated temperatures using micro Raman spectroscopy (MRS) and a time dependent shear-lag based single fiber composite model (SFM). The modeling parameters were obtained from the creep response of the unfilled epoxy at several stress levels and at temperatures up to 80°C. An effective fiber spacing was used in the model predictions to account for the radial decay of the interfacial shear stress from the fiber surface. Good agreement was observed between the model predictions and MRS data when the temperature dependence of _p (the shear stress in the matrix yielded zone) and _c (the critical shear strain for the onset of inelasticity) were taken into account. Overall, the inelastic length growing from the fiber fractures increases with temperature and time. This leads to a wider stress concentration profile in the neighboring intact fibers, which increases the chance of failure in the intact fibers and facilitates the creep-rupture process of the composite.     

Nondestructive Measurement of Fatigue Damage of Thermally Sprayed Al2O3/NiCr Using ESPI Method Under High Temperature

High-temperature fatigue (R = 0) damage and deformation behaviors of SUS304 steel thermally sprayed with an Al₂O₃/NiCr coating were investigated using a servopulse fatigue-testing machine, SEM, and an electronic speckle pattern interferometry (ESPI) method. The relation between crack/delamination and strain variation is discussed. Surface cracks occurred at the outer Al₂O₃ coating but stopped at the inner NiCr coating after one fatigue cycle when the tensile stress was 202 MPa at 873 K. They propagated into the NiCr coating but stopped at the substrate, and local delamination occurred along the NiCr/substrate interface after 1 × 10⁵ cycles test in condition (_max = 202 MPa, T = 873 K). Cracks and delamination largely decreased when _max = 115 MPa or T = 573 K. No influence of cycle frequencies (6.7 or 14 Hz) was detected. The strain value measured by ESPI method was confirmed to be almost the same as that obtained with strain gauges at 293 K. Strain values along cracks measured with the ESPI method were much larger than other areas as a result of crack opening under the tensile load, referred to as the strain concentration zone in this work. Positions of strain concentration zones on strain distribution figures by the ESPI method corresponded well to positions of cracks on sprayed coatings. Moreover, strain values largely decreased where local delamination occurred.     

Synthesis and Study of Sr[HSiUO6]2·2H2O and Ba[HSiUO6]2·2H2O

Uranosilicates of the general formula M^{I I}[HSiUO₆]₂·2H₂O (M^{I I} = Sr, Ba) were prepared by hydrothermal synthesis. Previously unknown intermediate crystal hydrates were separated and studied by X-ray diffraction (XRD), IR spectroscopy, and thermal analysis. Polymorphic transitions -Sr[HSiUO₆]₂ -Sr[HSiUO₆]₂ and -Ba[HSiUO₆]₂ -Ba[HSiUO₆]₂ were revealed at 700 and 780°C, respectively.     

Modeling of facesheet crack growth in titanium-graphite hybrid laminates. Part II: Experimental results

Titanium-graphite hybrid composite laminates exhibit a coupled damage growth mode of facesheet cracking and delamination. Part I of this work modeled the growth of the coupled damage mode. Fatigue experiments were conducted on single edge notch tension specimens to measure the crack growth rate. This paper compares the model predictions with experimental data. The three-dimensional finite element model successfully captured the damage growth behavior for two of the lay-ups ([Ti/0/90/0₂]_s and [Ti/90/0/90₂]_s) in the experimental program. However, in a third lay-up, [Ti/0/90/±30]_s, the underlying damage modes were found to be sufficiently different than the other two lay-ups and the model did not capture the steady-state growth behavior. The effects of temperature and specimen size were also investigated for TiGr laminates. Except for the effects of the load ratio, elevated temperatures did not affect the crack growth rate significantly. For wider specimens, the steady-state fatigue crack growth behavior was similar to the narrow specimens, indicating that the steady-state facesheet crack growth behavior is independent of specimen size.     

The mechanical behavior of optical fiber sensor embedded within the composite laminate

Mechanical behavior, such as tensile and fatigue strength, of the optical fiber sensor embedded within the composite laminate was investigated. Tensile and fatigue tests were performed to evaluate the static and fatigue characteristics of optical fibers embedded within three types of laminated composite specimens, [0₆/OF/0₆]_T, [0₂/90₄/OF/90₄/0₂]_T and [0₃/90₃/OF/90₃/0₃]_T. The initiation of damage and fracture of the optical fiber were detected by observation of the intensity drop-off of laser signal transmitted through the optical fiber during test. Experimental results showed that the fatigue strength of optical fiber embedded within the cross-ply laminate is much lower than the fatigue strength of optical fiber within the unidirectional ply laminate. It was also found that the optical fiber embedded within unidirectional ply laminate fractured due to the fatigue damage accumulation of internal defects of optical fiber itself. However the optical fiber embedded within the cross-ply laminate fractured due to the growth of transverse matrix crack of host composite laminate.