We present a statistical analysis based methodology for making assessment of the manufacturing quality of cross ply composite laminates as it relates to its effect on transverse cracking evolution. ...Assuming a two-parameter Weibull distribution of tensile strength of the transverse plies to represent randomly distributed manufacturing defects, multiple crack formation in the plies is simulated in the non-interactive and interactive regimes of cracking using the local stress fields calculated by a variational analysis. The statistical methodology is demonstrated on crack density evolution in cross ply laminates manufactured by four different processing routes and loaded in monotonic tension in the axial direction. The differences in the crack density evolution, supposedly due to different defect population induced by the four manufacturing conditions, could be described by the proposed statistical simulation method.
The continuum damage mechanics (CDM) model by Talreja Talreja R. Damage characterization by internal variables. In: Pipes RB, Talreja R, editors. Comput Mater Series, vol. 9. Dam Mech Comp Mater, ...Elsevier, Amsterdam; 1994, p. 53–78, which is one of the most efficient for damaged laminate stiffness determination, is analyzed using earlier developed theoretical framework which links the macro-response of a damaged laminate to the opening and sliding displacements of crack surfaces in an exact form. The physical meaning of the material parameters in CDM is revealed. Exact expressions for these parameters are derived and transformation rules with changing layer orientation angle presented. These parameters were previously considered as the most troublesome part of the CDM model with need for additional tests for their determination. The error introduced by the two main assumptions in the CDM model ((a) stiffness change is linear with respect to damage tensor, (b) crack face sliding effect can be neglected) is evaluated and found that the linearization is often justified but sliding cannot be neglected in most of the lay-ups.
The objective of this work is to evaluate the effect of residual thermal stresses, arising after assembling a single-lap joint at elevated temperature, on the inelastic thermo-mechanical stress state ...in the adhesive layer. The numerical analysis (FEM) employing linear and non-linear material models, with geometrical nonlinearity accounted for, is carried out. Simulating the mechanical response, the calculated thermal stresses are assigned as initial conditions to polymeric, composite and metallic joint members to reflect the loading sequence where the mechanical strain is applied to cooled-down structure. It is shown that the sequence of application matters and simulations with simultaneous application of temperature and strain give different result. Two scenarios for adhesive joints with composites are studied: joining by adhesive curing of already cured composite parts (two-step process) and curing the adhesive and the composite simultaneously in one-step (co-curing). Results show that while in-plane stresses in the adhesive are higher, the peaks of out-of-plane shear stress and peel stress (most responsible for the joint failure) at the end of the overlap are reduced due to thermal effects. In joints containing composite parts, the one-step joining scenario is more favorable than the two-step. The ply stacking sequence in the composite has significant effect on stress concentrations as well as on the plateau value of the shear stress in the adhesive.
It is shown, using thermodynamically consistent linear viscoelastic material model that accounts for properties dependence on test temperature and cure state parameters, that for rheologically simple ...materials the cure and temperature related reduced times and shift factors are the same for all viscoelastic compliances, relaxation modulus, and Poisson's ratio as well as for the storage and loss modulus. A necessary condition for that is that the cure and temperature parameters are affecting the reduced time only. This means that the Poisson's ratio of polymeric materials, which for simplicity is often assumed constant, in fact exhibits a small dependence on time which is affected by temperature and state of cure. In this work, the evolution of the viscoelastic Poisson's ratio of the commercial LY5052 epoxy resin is studied in relaxation test subjecting the specimen to constant axial strain. Specimens at several cure states are studied and Poisson's ratio, defined as the lateral and axial strain ratio, is shown to evolve from 0.32 to 0.44 over time. Moreover, the data confirm that the cure state-dependent reduced time controlling the Poisson's ratio development leads to the same shift functions as those identified in DMTA tests for storage modulus. The latter measurements also confirmed that the total shift can be considered as a sum of two shifts in the frequency domain, which means that function for reduced time calculation can be written as a product of two functions: one dependent on the test temperature and another one dependent on the cure state.
A thermo-rheologically complex linear viscoelastic material model, accounting for temperature and degree of cure (DoC), is developed starting with series expansion of the Helmholtz free energy and ...systematically implementing simplifying assumptions regarding the material behavior. In addition to the temperature and DoC dependent shift factor present in rheologically simple models, the derived novel model contains three cure and temperature dependent functions. The first function is identified as the rubbery modulus. The second is a weight factor to the transient integral term in the model and reflects the current temperature and cure state, whereas the third function is under the sign of the convolution integral, thus affecting the "memory" of the material. An incremental form of this model is presented which, due to improved approximation inside the time increment, has better numerical convergence than most of the similar forms. Parametric analysis is performed simulating stress development in a polymer, geometrically constrained in the mold during curing and cool-down. The importance of using proper viscoelastic model is shown, and the role of parameters in the model is revealed and discussed.
This article is the author’s contribution to the third World-Wide Failure Exercise which aims at benchmarking current damage models for composites. Reduction of thermo-elastic constants of laminates ...and their nonlinear behaviour due to intralaminar cracking and nonlinear shear response of the composite are analysed using global–local approach. The macroscopic properties of damaged laminates are expressed in simple forms containing density of intralaminar cracks and their surface displacement features obtained from local solutions. The initiation and evolution of the intralaminar damage is analysed using strength-based approach for laminates with thick layers and fracture mechanics approach for thin layers. Due to a lack of information, certain characteristics, such as statistical failure properties distribution parameters and transition point (thickness) from strength to fracture mechanics applicability, were assumed. All calculations are based on analytical expressions, some of which were developed previously through numerical analysis. The present method was applied to solve 9 out of the 13 test cases of the third World-Wide Failure Exercise and that was sufficient to illustrate the capability of the damage model.
In this paper propagation of matrix cracks and debonds at the coating/matrix interface in the 90°-layer of a cross-ply structural composite battery are studied numerically. The structural composite ...battery consists of micro-battery units, made of a solid electrolyte coated carbon fiber embedded in an electrochemically active polymer matrix. During charging the fiber swells and the matrix shrinks leading to high stresses on the fiber/matrix scale and to anisotropic free expansion of the composite ply. Two load cases are considered, pure electrochemical load (intercalation) and combined electrochemical and thermomechanical load. Energy release rates (ERR) of radial matrix cracks along two potential propagation paths are calculated using 2-D finite element models of the transverse plane in a cross-ply laminate with a square packing of fibers in the 90°-ply and using homogenized 0°-ply. Results show that the matrix crack growth towards the nearest fiber is unstable, and that the debond crack growth is in mixed mode. For a cross-ply structural battery composite the sequence of macro-scale crack forming events differs from a conventional cross-ply composite, as well as for a UD composite battery laminate. The most likely course of failure events in a cross-ply laminate are: 1) vertical radial matrix crack initiation and unstable growth; 2) debond is initiated at certain length of the matrix crack.
The aim of this work is to develop a methodology to analyze the influence of the curing history on the viscoelastic storage modulus. Two different experimental approaches are presented exposing the ...material to various cure temperature and cure time sequences. The evolving viscoelastic properties are characterized using standard Dynamic Mechanical and Thermal Analysis (DMTA) equipment. Therefore, the present study is limited to infinitesimally small strains and linear viscoelasticity only. The methodology is demonstrated using the LY5052 epoxy resin system for its storage modulus E′ in the frequency domain. Results indicate that evolution of thermo-viscoelastic properties could be indeed assumed independent of the cure history for the investigated LY5052. We observe that the shift factor in the reduced time expression for the viscoelastic model examined in this paper is a product of two shift functions, namely the temperature and cure shift functions.
Thermo-mechanical response of 90n/0ms carbon/epoxy and glass/epoxy cross-ply laminates in 4-point bending is analyzed experimentally and analytically. Intralaminar cracks in surface 90°-plies and ...local delaminations introduced in one of the 90°-plies at large deflections reduce the laminate bending stiffness and make the laminate asymmetric due to differences in the damage state in the layers. The latter leads to residual thermal curvature that increases with intralaminar crack density and with growing local delaminations. In the present study optical microscopy was used for crack density quantification. It was also found experimentally that small local delaminations develop in the initial stage of damage evolution and under increasing load they grow rapidly from the existing and newly created crack tips. The effect of damage on residual curvature and the bending stiffness was analyzed using an analytical method, where the concept of the effective stiffness of damaged ply is used in the classical laminate theory. Analytical results were validated with a 3-D FEM simulation of the damaged laminate in a 4-point bending test. In the literature a phenomenon that the microdamage in laminate layers causes redistribution of in-plane thermal stresses is often overlooked. The present paper shows that the used analytical approach gives an accurate description of experimental results regarding two independent sets of data: the residual curvature; and the laminate bending stiffness with evolving micro-damage. The present study also renders a better insight in the mechanics of the phenomena and allows estimation of the extent of local delaminations that is difficult to measure in tests.
The effect of the helical wood fiber structure on in-plane composite properties has been analyzed. The used analytical concentric cylinder model is valid for an arbitrary number of phases with ...monoclinic material properties in a global coordinate system. The wood fiber was modeled as a three concentric cylinder assembly with lumen in the middle followed by the S3, S2 and S1 layers. Due to its helical structure the fiber tends to rotate upon loading in axial direction. In most studies on the mechanical behavior of wood fiber composites this extension-twist coupling is overlooked since it is assumed that the fiber will be restricted from rotation within the composite. Therefore, two extreme cases, first modeling fiber then modeling composite were examined: (i) free rotation and (ii) no rotation of the cylinder assembly. It was found that longitudinal fiber modulus depending on the microfibril angle in S2 layer is very sensitive with respect to restrictions for fiber rotation. In-plane Poisson’s ratio was also shown to be greatly influenced. The results were compared to a model representing the fiber by its cell wall and using classical laminate theory to model the fiber. It was found that longitudinal fiber modulus correlates quite well with results obtained with the concentric cylinder model, whereas Poisson’s ratio gave unsatisfactory matching. Finally using typical thermoset resin properties the longitudinal modulus and Poisson’s ratio of an aligned softwood fiber composite with varying fiber content were calculated for various microfibril angles in the S2 layer.
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