Size Effect and Fracture Characteristics of Composite Laminates

1996 ◽  
Vol 118 (3) ◽  
pp. 317-324 ◽  
Author(s):  
Zdeneˇk P. Bazˇant ◽  
Isaac M. Daniel ◽  
Zhengzhi Li
Keyword(s):  
Size Effect ◽  
Composite Laminates ◽  
Process Zone ◽  
Fiber Composite ◽  
Maximum Load ◽  
Two Dimensions ◽  
Effective Length ◽  
Smooth Transition ◽  
Fracture Characteristics ◽  
Nominal Strength

Measurements of the size effect on the nominal strength of notched specimens of fiber composite laminates are reported. Tests were conducted on graphite/epoxy crossply and quasi-isotropic laminates. The specimens were rectangular strips of widths 6.4, 12.7, 25.4 and 50.8 mm (0.25, 0.50, 1.00 and 2.00 in.) geometrically similar in two dimensions. The gage lengths were 25, 51, 102 and 203 mm (1.0, 2.0, 4.0 and 8.0 in.). One set of specimens had double-edge notches and a [0/922]s crossply layup, and another set had a single-sided edge notch and a [0/±45/90]s, quasi-isotropic layup. It has been found that there is a significant size effect on the nominal strength. It approximately agrees with the size effect law proposed by Bazˇant, according to which the curve of the logarithm of the nominal strength versus the logarithm of size represents a smooth transition from a horizontal asymptote, corresponding to the strength criterion (plastic limit analysis), to an inclined asymptote of −0.5 slope, corresponding to linear elastic fracture mechanics. Optimum fits of the test results by the size effect law are obtained, and the size effect law parameters are then used to identify the material fracture characteristics, particularly the fracture energy and the effective length of the fracture process zone. Finally, the R-curves are also identified on the basis of the maximum load data. The results show that in design situations with notches or large initial traction-free cracks the size effect on the nominal strength of fiber composite laminates must be taken into account.

scholarly journals Scaling of Quasi-Brittle Fracture and the Fractal Question

1995 ◽  
Vol 117 (4) ◽  
pp. 361-367 ◽  
Author(s):  
Zdeneˇk P. Bazˇant
Keyword(s):  
Size Effect ◽  
Composite Laminates ◽  
Process Zone ◽  
Asymptotic Properties ◽  
Material Strength ◽  
Fractal Nature ◽  
Quasibrittle Materials ◽  
Large Size ◽  
Fracture Simulation ◽  
Nominal Strength

The paper represents an extended text of a lecture presenting a review of recent results on scaling of failure in structures made of quasibrittle materials, characterized by a large fracture process zone, and examining the question of possible role of the fractal nature of crack surfaces in the scaling. The problem of scaling is approached through dimensional analysis, the laws of thermodynamics and asymptotic matching. Large-size and small-size asymptotic expansions of the size effect on the nominal strength of structures are given, for specimens with large notches (or traction-free cracks) as well as zero notches, and simple size effect formulas matching the required asymptotic properties are reported. The asymptotic analysis is carried out, in general, for fractal cracks, and the practically important case ofnonfractal crack propagation is acquired as a special case. Regarding the fractal nature of crack surfaces in quasibrittle materials, the conclusion is that it cannot play a signification role in fracture propagation and the observed size effect. The reason why Weibull statistical theory of random material strength does not explain the size effect in quasibrittle failures is explained. Finally, some recent applications to fracture simulation by particle models (discrete element method) and to the determination of size effect and fracture characteristics of carbon-epoxy composite laminates are briefly reviewed.

scholarly journals Size Effect in Fracture of Sandwich Structure Components: Foam and Laminate

2001 ◽  
Author(s):  
Zdeněk P. Bažant ◽  
Yong Zhou ◽  
Drahomír Novák ◽  
Isaac M. Daniel
Keyword(s):  
Size Effect ◽  
Size Effects ◽  
Sandwich Structure ◽  
Maximum Load ◽  
Material Strength ◽  
Large Structures ◽  
Nominal Strength ◽  
Sandwich Plates And Shells ◽  
Extensive Test ◽  
Plates And Shells

Abstract In the design of sandwich plates and shells for very large structures, such as ships in the range of 100 m length, it is very important to take the size effect on the nominal strength into account, and do so in a realistic, physically justified, manner. Before the size effect is addressed for a sandwich structure, it must be understood for its components — the foam core and the laminate skins. In the current practice, the size effects are automatically attributed to the randomness of material strength, as described by the Weibull theory. The purpose of this paper is to show that in both the foam and the laminate there are deterministic size effects, which are generally more pronounced. They are caused by stress redistribution and energy release due to the growth of large fractures or large cracking zones prior to attaining the maximum load. This deterministic size effect is verified and calibrated by new tests of notched specimens of rigid close-cell vinyl foam. A combined deterministic-probabilistic theory of size effect of the laminates is proposed and verified by extensive test data.

Fishnet Statistical Size Effect on Strength of Materials With Nacreous Microstructure

2019 ◽  
Vol 86 (8) ◽  
Author(s):  
Wen Luo ◽  
Zdeněk P. Bažant
Keyword(s):  
Size Effect ◽  
Failure Probability ◽  
Maximum Load ◽  
Strength Distribution ◽  
Strength Limit ◽  
Nominal Strength ◽  
Geometric Scaling ◽  
Simple Scaling ◽  
Structure Strength ◽  
Architectured Materials

The statistical size effect has generally been explained by the weakest-link model, which is valid if the failure of one representative volume element (RVE) of material, corresponding to one link, suffices to cause failure of the whole structure under the controlled load. As shown by the recent formulation of fishnet statistics, this is not the case for some architectured materials, such as nacre, for which one or several microstructural links must fail before reaching the maximum load or the structure strength limit. Such behavior was shown to bring about major safety advantages. Here, we show that it also alters the size effect on the median nominal strength of geometrically scaled rectangular specimens of a diagonally pulled fishnet. To derive the size effect relation, the geometric scaling of a rectangular fishnet is split into separate transverse and longitudinal scalings, for each of which a simple scaling rule for the median strength is established. Proportional combination of both then yields the two-dimensional geometric scaling and its size effect. Furthermore, a method to infer the material failure probability (or strength) distribution from the median size effect obtained from experiments or Monte Carlo simulations is formulated. Compared to the direct estimation of the histogram, which would require more than ten million test repetitions, the size effect method requires only a few (typically about six) tests for each of three or four structure sizes to obtain a tight upper bound on the failure probability distribution. Finally, comparisons of the model predictions and actual histograms are presented.

scholarly journals The role of the material fracture properties in the size-effect law of concrete structures

1996 ◽  
Vol 18 (1) ◽  
pp. 40-48
Author(s):  
V. Tran Tu
Keyword(s):  
Size Effect ◽  
Process Zone ◽  
Crack Opening ◽  
Concrete Structures ◽  
Fracture Propagation ◽  
Fracture Properties ◽  
Nominal Strength ◽  
Material Fracture ◽  
General Size

The size effect of the nominal stress at failure in concrete structures is dealt within general. An existence of a rather large fracture process zone in front of crack tip is proved to be the main reason leading to the size effect of the nominal strength. On the basis of the new general size-effect law and numerical results of fracture propagation, a particularly proposed size effect law for beams in bending is developed, in which the role of each material fracture characteristic, especially the shape of the stress - crack opening curve, is elaborated clearly.

Effect of stacking sequence and geometric scaling on the brittleness number of glass fiber composite laminate with stress raiser

2014 ◽  
Vol 21 (2) ◽  
pp. 281-288 ◽  
Author(s):  
Y. Mohammed ◽  
Mohamed K. Hassan ◽  
Abu El-Ainin H ◽  
A.M. Hashem
Keyword(s):  
Glass Fiber ◽  
Composite Laminates ◽  
Fiber Composite ◽  
Stress Raiser ◽  
Compact Tension ◽  
Tension Test ◽  
Center Crack ◽  
Nominal Strength ◽  
Geometric Scaling ◽  
Brittleness Number

AbstractThe fracture behavior of quasi-brittle material exhibits commonly brittle behavior with some ductility in the fracture processing zone. Therefore, a matrix of experimental works is performed to investigate the failure behaviors based on a parameter known as brittleness number, which is a measure of brittle behaviors. Glass fiber-reinforced epoxy laminates of three stacking sequences, cross-ply [0/90]2s and two quasi-isotropic [0/45/90]2s and [0/45/90/-45]s, are manufactured using hand lay-up technique. A matrix of different specimen geometric scaling with open hole of the same material is used. The fracture energy GIC and nominal strength of these composite laminates are measured experimentally using compact tension test, center crack specimen, and tension test, respectively. The results showed that the increase of homogeneity of composite laminates, which is introduced by inserting a certain angle ply for the laminate structure, enhanced the material ductility as the brittle number increased. The larger size of specimen leads to the increase of brittleness for the same stacking sequences due to the increase of stress concentration factor.

scholarly journals Size Effect in Fracture of Concrete Specimens and Structures: New Problems and Progress

10.14311/608 ◽  
2004 ◽  
Vol 44 (5-6) ◽  
Author(s):  
Z. P. Bažant ◽  
Q. Yu
Keyword(s):  
Size Effect ◽  
Fracture Energy ◽  
Damage Model ◽  
Apparent Size ◽  
Shear Capacity ◽  
Cohesive Crack ◽  
Smooth Transition ◽  
Crack Model ◽  
Cohesive Crack Model ◽  
Nominal Strength

Presented is a concise summary of recent Northwestern University studies of six new problems. First, the decrease of fracture energy during crack propagation through a boundary layer, documented by Hu and Wittmann, is shown to be captured by a cohesive crack model in which the softening tail slope depends on the distance from the boundary (which causes an apparent size effect on fracture energy and implies that the nonlocal damage model is more fundamental than the cohesive crack model). Second, an improved universal size effect law giving a smooth transition between failures at large cracks (or notches) and at crack initiation is presented. Third, a recent renewed proposal that the nominal strength variation as a function of notch depth be used for measuring fracture energy is critically examined. Fourth, numerical results and a formula describing the size effect of finite-angle notches are presented. Fifth, a new size effect law derivation from dimensional analysis coupled with asymptotic matching is given. Finally, an improved code-type formula for shear capacity of R.C. beams is proposed. 

An approximate analytical model for modification of size effect law for open-hole composite structure under biaxial load

2020 ◽  
pp. 095440622095937
Author(s):  
Mohammed Y Abdellah
Keyword(s):  
Size Effect ◽  
Composite Laminates ◽  
Approximate Model ◽  
Biaxial Stress ◽  
Damage Initiation ◽  
Main Challenge ◽  
Nominal Strength ◽  
Biaxial Stress State ◽  
Cohesive Laws ◽  
Open Hole

Nominal strength prediction remains the main challenge in the field of design and manufacturing of composite laminates. An approximate model to study the stress distribution around a circular hole in composite laminates is derived in this study. This model is constructed using well-known cohesive zone models and mainly depends on the un-notch strength and in-plane fracture toughness. The model attempts to modify and extend the specimen size effect curves, extracted using two-parameter cohesive laws (linear, exponential, and constant), into a biaxial stress state. It successfully predicts the damage initiation, propagation, and fracture of multidirectional composite laminates. Moreover, the stress concentration factor for a composite plate under varying biaxiality is calculated.

scholarly journals Mode I and II Interlaminar Fracture in Laminated Composites: A Size Effect Study

2019 ◽  
Vol 86 (9) ◽  
Author(s):  
Marco Salviato ◽  
Kedar Kirane ◽  
Zdeněk P. Bažant ◽  
Gianluca Cusatis
Keyword(s):  
Size Effect ◽  
Process Zone ◽  
Laminated Composites ◽  
Nonlinear Effects ◽  
Effect Study ◽  
Mode I ◽  
Brittle Behavior ◽  
Linear Elastic ◽  
Nominal Strength ◽  
Significant Difference

This work investigates the mode I and II interlaminar fracturing behavior of laminated composites and the related size effects. Fracture tests on geometrically scaled double cantilever beam (DCB) and end notch flexure (ENF) specimens were conducted. The results show a significant difference between the mode I and mode II fracturing behaviors. The strength of the DCB specimens scales according to the linear elastic fracture mechanics (LEFM), whereas ENF specimens show a different behavior. For ENF tests, small specimens exhibit a pronounced pseudoductility. In contrast, larger specimens behave in a more brittle way, with the size effect on nominal strength closer to that predicted by LEFM. This transition from quasi-ductile to brittle behavior is associated with the size of the fracture process zone (FPZ), which is not negligible compared with the specimen size. For the size range investigated in this study, the nonlinear effects of the FPZ can lead to an underestimation of the fracture energy by as much as 55%. Both the mode I and II test data can be captured very accurately by the Bažant’s type II size effect law (SEL).

Microstructure and Fracture of Engineering Polymers and Composites

1986 ◽  
Vol 79 ◽  
Author(s):  
K. Friedrich
Keyword(s):  
Composite Laminates ◽  
Volume Fraction ◽  
Fiber Composite ◽  
Short Fiber ◽  
Related Factors ◽  
Fracture Characteristics ◽  
Microstructural Parameters ◽  
Reinforcing Fibers ◽  
Injection Molded ◽  
Engineering Polymers

AbstractThe fracture properties of engineering polymers and composites are strongly affected by two major areas of influence. The first one covers the microstructural parameters of the material, whereas the second one includes the external testing conditions. In this contribution, it is mainly outlined how area one can determine the fracture characteristics. An introductory section illustrates the variety of microstructural details, for example molecular structure and semicrystalline polymer morphology, and filler related factors, such as volume fraction of reinforcing fibers, their orientation etc. In the following part, effects of these parameters on fracture mechanical properties are discussed. It is distinguished between the fracture behavior of unfilled engineering polymers, of short fiber reinforced, injection molded thermoplastics, and of continuous fiber composite laminates. In the latter group, special emphasis is given to the effect of new, high temperature resistant thermoplastic matrices, for instance PEEK, on the interlaminar fracture energy of the composites.

Scaling of Strength of Metal-Composite Joints—Part I: Experimental Investigation

2009 ◽  
Vol 77 (1) ◽  
Author(s):  
Qiang Yu ◽  
Zdeněk P. Bažant ◽  
John Bayldon ◽  
Jia-Liang Le ◽  
Ferhun C. Caner ◽  
...  
Keyword(s):  
Size Effect ◽  
Peak Load ◽  
Maximum Load ◽  
Lap Joints ◽  
Interface Fracture ◽  
Metal Composite ◽  
Interface Failure ◽  
Interface Shear ◽  
Nominal Strength ◽  
The University

Knowledge of the size effect on the strength of hybrid bimaterial joints of steel and fiber composites is important for new designs of large lightweight ships, large fuel-efficient aircrafts, and lightweight crashworthy automobiles. Three series of scaled geometrically similar specimens of symmetric double-lap joints with a rather broad size range (1:12) are manufactured. The specimens are tested to failure under tensile displacement-controlled loading, and at rates that ensure the peak load to be reached within approximately the same time. Two series, in which the laminate is fiberglass G-10/FR4, are tested at Northwestern University, and the third series, in which the laminate consists of NCT 301 carbon fibers, is tested at the University of Michigan. Except for the smallest specimens in test series I, all the specimens fail by propagation of interface fracture initiating at the bimaterial corner. All the specimens fail dynamically right after reaching the maximum load. This observation confirms high brittleness of the interface failure. Thus, it is not surprising that the experiments reveal a marked size effect, which leads to a 52% reduction in nominal interface shear strength. As far as the inevitable scatter permits it to see, the experimentally observed nominal strength values agree with the theoretical size effect derived in Part II of this study, where the size exponent of the theoretical large-size asymptotic power law is found to be −0.459 for series I and II, and −0.486 for series III.

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