A Stochastic Model for the Growth of Matrix Cracks in Composite Laminates

Wang, A.S.D.; Chou, Pei Chi; Lei, Shi

doi:10.1177/002199838401800304

Cited by 124 publications

(42 citation statements)

References 4 publications

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“…A The simulation performed in this study differed from those of other studies, such as Wang's [27]. Instead of assuming a flaw size distribution in the transverse layer, we simulated the crack multiplication by partitioning the initial gage length into 5000 equal elements and assigning a strength value to each element in accordance with our experimental distribution function.…”

Section: Transverse Cracking -Statistical Modelmentioning

confidence: 99%

“…They also pointed out that if the matrix is completely homogeneous in strength, the cracks will always form at the midpoint of the segments. In this case, they can determine the probability density function (PDF) of crack spacing, which is f(/,/ 0 ) = / 0 /r (27) where l 0 is the crack spacing corresponding to a specific applied stress a x .…”

Section: Transverse Cracking -Statistical Modelmentioning

confidence: 99%

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Constitutive Behavior and Damage Characterization of High Temperature Polymer Composites

Daniel¹,

Luo²,

Sun³

2001

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REPORT DOCUMENTATION PAGEPublic reporting burden for this collection of information is estimated to average 1 hour per response, including the fimerfor reviewinj dS needed and completinq and reviewing this collection of information. Send comments regarding this burden estimate or any ott 4302 Respondents should be aware that notwithstanding any other provfeion of law no person shall be subject to any penalty for f, valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. _ AFRL-SR-BL-TR-01-igthe ucing 02-jrrently REPORT DATE (DD-MM-YYYY) 31-08-2001 REPORT TYPE Final TITLE AND SUBTITLE Constitutive Behavior and Damage Characterization of High Temperature Polymer Composites AUTHOR(S)Isaac M. Daniel, Jyi-Jiin Luo and Zuo Sun PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)Northwestern University Evanston, EL 60208 DATES COVERED (From -To)Oct. 15.199715. -April 14,2001 5a. CONTRACT NUMBER 5b. GRANT NUMBER F49620-98-1-0056 5c. PROGRAM ELEMENT NUMBER 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER SPONSORING / MONITORING AGENCY NAME(S) AND ADDRESS(ES)Air Force Office of Scientific Research (AFOSR) Arlington, VA 22203-1977 PERFORMING ORGANIZATION REPORT NUMBERC416-4 . t . , , The objective of this investigation was to characterize the constitutive behavior, physical aging, damage mechanisms and damage development in high temperature polymer matrix composites under various environmental and loading conditions. The aging induced volumetric shrinkage was measured and a model was proposed capable of predicting aging under any temperature history. In the case of monotonically loaded laminates a unique and simple general relationship was developed between applied load and crack density independent of lamination geometry and temperature and accounting for statistical variability. Under fatigue conditions a master curve was developed relating damage (crack density) and fatigue cycles, independent of layup and temperature. It is related to and affected by physical aging of the polymeric matrix, viscoelastic deformation (creep) and hygrothermomechanical degradation. It is therefore important to investigate the processes involved and any accelerated test methodologies that will yield valid predictions of long term behavior. SPONSOR/MONITOR'S ACRONYM(S) SPONSOR/MONITOR'S REPORT NUMBER(S) DISTRIBUTION / AVAILABILITY STATEMENT Distribution unlimited SUPPLEMENTARY NOTES ABSTRACTt ,The objective of this investigation is to characterize the constitutive behavior, damage mechanisms and damage development in high temperature polymer matrix composites and develop models for long term behavior under various environmental and loading conditions. The approach followed is as follows:1. Select candidate polymer composite materials. 2.Characterize unidirectional lamina. 3.Perform aging and viscoelastic characterization under isothermal and nonisothermal conditions. 4.Study static and fatigue behavior of laminae and laminates at various cyclic stress amplitudes and temperature levels. 5.Study failure mode...

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Section: Transverse Cracking -Statistical Modelmentioning

confidence: 99%

Section: Transverse Cracking -Statistical Modelmentioning

confidence: 99%

Constitutive Behavior and Damage Characterization of High Temperature Polymer Composites

Daniel¹,

Luo²,

Sun³

2001

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“…The interaction of transverse cracking, cracks which initiate randomly at matrix voids, and delamination causes quite an irregular fracture surface (i.e. delamination) and follows a completely random path that is contained by the two interfaces of the 90°-layer [39][40][41][42][43][44][45]. The delamination itself progresses abruptly and intermittently [39][40] with increasing load, although it might not extend across the specimen's width [40].…”

Section: 4mentioning

confidence: 99%

“…Similar observations were reported in [43], where this relationship is attributed to the constraining effect of the neighboring 00 layers. The transverse ply cracking strain is also affected by the thickness of the [ 0 4/ 9 0 8/ 0 4]T and may decrease from 0.0065 to 0.003 for [04/90n/04]T and [ 0 4/ 9 0 8/04]T, respectively, graphite/epoxy laminates [42]. It was concluded that "it is the total strain energy trapped in the 90*-layer which determines the onset of cracking, not the in-situ tensile stress" [44].…”

Section: 4mentioning

confidence: 99%

“…Comparison between the rate of accumulation of transverse cracks in [ 0 2/ 9 0 2]s and in [ 0 2/ 9 0 3]s graphite/epoxy laminates indicates that the thicker the transverse ply is, the lower the cycle number at which transverse cracking initiates [42]. It should be noted that these cracks occur at fatigue stress levels which are much below the quasi-static threshold levels at which they appear.…”

Section: 4mentioning

confidence: 99%

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Detection of failure progression in cross-ply graphite/epoxy during fatigue through acoustic emission. Volume 1

Awerbuch¹,

Eckles²,

Erdman³

1992

NDT & E International

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An extended Layerwise method for composite laminated beams with multiple delaminations and matrix cracks

Liu

Zhang

2014

Numerical Meth Engineering

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For the delamination and matrix crack prediction of composite laminated structures, the methods based on the damage mechanics and fracture mechanics are most commonly used. However, there are very few methods that can accurately simulate the delaminations together with matrix cracks, although the in-plane matrix cracks always exist alongside the delaminations under impact loading. In this work, an extended layerwise method is developed to model the composite laminated beam with multiple delaminations and matrix cracks. In the displacement field, the nodes in the thickness direction are located at the middle surface of each single layer, the top surface and the bottom surface of the composite beams. The displacement field contains the linear Lagrange interpolation functions, the one-dimensional weak discontinuous function and strong discontinuous function. The strong and weak discontinuous function are applied to model the displacement discontinuity induced by delaminations and the strain discontinuity induced by the interface between the layers, respectively. Because the nodes in the thickness direction are located at the middle surface of each single layer, the extended layerwise method can be conveniently employed to deal with the in-plane matrix cracks combined with the extend FEM. Figure 1. Typical matrix cracks and delaminations pattern resulted from low impact [12].delamination by macro-scopic damage initiation criteria, such as Choi-Wu [6,7] and Hashin criteria [22,23]. The cumulative effect of delamination can be described by the material degradation models at failure material point. The implementation of the damage mechanics methods is very simple. Because the damage is incorporated within the constitutive model, the damage mechanics methods are easily adapted to numerical approaches such as the FEM. But the real extension process of delamination can not be observed in the damage mechanics methods. In the fracture mechanics methods, linear elastic fracture mechanics (LEFM) is commonly applied for the problem of delamination. Although the fracture mechanics predictions for metallic materials has been widely adopted because of its relative simplicity and accuracy, it is not true for the delamination problem of composite laminates. LEFM is only suited to bonded composite where a realistic de-bonded defect can be defined and the loads produce a uniform linear strain regime. The cohesive fracture model addresses some of the limitations of LEFM, such as the material softening at the crack front and the damage initiation of the delamination in monolithic composites. For the fracture mechanics, the sensitivity to mesh shape still exists and will limit the applicability to the impact problems when used in conjunction with current nonadaptive FE methods. The primary advantage of the fracture mechanics methods is that fracture mechanics concepts can be readily incorporated, such as critical energy release rate. However, the adaptation of the fracture mechanics methods to FEA is somewhat more complicated, because it...

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A Stochastic Model for the Growth of Matrix Cracks in Composite Laminates

Cited by 124 publications

References 4 publications

Constitutive Behavior and Damage Characterization of High Temperature Polymer Composites

Constitutive Behavior and Damage Characterization of High Temperature Polymer Composites

Detection of failure progression in cross-ply graphite/epoxy during fatigue through acoustic emission. Volume 1

An extended Layerwise method for composite laminated beams with multiple delaminations and matrix cracks

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