scholarly journals Size Effect of Cohesive Delamination Fracture Triggered by Sandwich Skin Wrinkling

2007 ◽  
Vol 74 (6) ◽  
pp. 1134-1141 ◽  
Author(s):  
Zdeněk Bažant ◽  
Peter Grassl
Keyword(s):  
Size Effect ◽  
Impact Analysis ◽  
Cohesive Crack ◽  
Crack Model ◽  
Element Analysis ◽  
Simple Description ◽  
Nominal Strength ◽  
Delamination Fracture ◽  
Special Cases ◽  
Asymptotic Matching

Because the observed size effect follows neither the strength theory nor the linear elastic fracture mechanics, the delamination fracture of laminate-foam sandwiches under uniform bending moment is treated by the cohesive crack model. Both two-dimensional geometrically nonlinear finite element analysis and one-dimensional representation of skin (or facesheet) as a beam on elastic-softening foundation are used. The use of the latter is made possible by realizing that the effective elastic foundation stiffness depends on the ratio of the critical wavelength of periodic skin wrinkles to the foam core thickness, and a simple description of the transition from shortwave to longwave wrinkling is obtained by asymptotic matching. Good agreement between both approaches is achieved. Skin imperfections (considered proportional to the the first eigenmode of wrinkling), are shown to lead to strong size dependence of the nominal strength. For large imperfections, the strength reduction due to size effect can reach 50%. Dents from impact, though not the same as imperfections, might be expected to cause as a similar size effect. Using proper dimensionless variables, numerical simulations of cohesive delamination fracture covering the entire practical range are performed. Their fitting, heeding the shortwave and longwave asymptotics, leads to an approximate imperfection-dependent size effect law of asymptotic matching type. Strong size effect on postpeak energy absorption, important for impact analysis, is also demonstrated. Finally, discrepancies among various existing formulas for critical stress at periodic elastic wrinkling are explained by their applicability to different special cases in the shortwave-longwave transition.

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. 

Scaling of Strength of Metal-Composite Joints—Part II: Interface Fracture Analysis

2009 ◽  
Vol 77 (1) ◽  
Author(s):  
Jia-Liang Le ◽  
Zdeněk P. Bažant ◽  
Qiang Yu
Keyword(s):  
Size Effect ◽  
Crack Length ◽  
Interface Crack ◽  
Fiber Composite ◽  
Preceding Paper ◽  
Cohesive Crack ◽  
Crack Model ◽  
Metal Composite ◽  
Composite Joint ◽  
Nominal Strength

The effect of the size of hybrid metal-composite joint on its nominal strength, experimentally demonstrated in the preceding paper (part I), is modeled mathematically. Fracture initiation from a reentrant corner at the interface of a metallic bar and a fiber composite laminate sheet is analyzed. The fracture process zone (or cohesive zone) at the corner is approximated as an equivalent sharp crack according to the linear elastic fracture mechanics (LEFM). The asymptotic singular stress and displacement fields surrounding the corner tip and the tip of an interface crack emanating from the corner tip are calculated by means of complex potentials. The singularity exponents of both fields are generally complex. Since the real part of the stress singularity exponent for the corner tip is not −12, as required for finiteness of the energy flux into the tip, the interface crack propagation criterion is based on the singular field of the interface crack considered to be embedded in a more remote singular near-tip field of the corner from which, in turn, the boundaries are remote. The large-size asymptotic size effect on the nominal strength of the hybrid joint is derived from the LEFM considering the interface crack length to be much smaller than the structure size. The deviation from LEFM due to finiteness of the interface crack length, along with the small-size asymptotic condition of quasiplastic strength, allows an approximate general size effect law for hybrid joints to be derived via asymptotic matching. This law fits closely the experimental results reported in the preceding paper. Numerical validation according to the cohesive crack model is relegated to a forthcoming paper.

scholarly journals An embedded cohesive crack model for finite element analysis of brickwork masonry fracture

2009 ◽  
Vol 76 (12) ◽  
pp. 1930-1944 ◽  
Author(s):  
E. Reyes ◽  
J.C. Gálvez ◽  
M.J. Casati ◽  
D.A. Cendón ◽  
J.M. Sancho ◽  
...  
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Cohesive Crack ◽  
Crack Model ◽  
Cohesive Crack Model ◽  
Element Analysis

scholarly journals Critical comparison of the boundary effect model with cohesive crack model and size effect law

2019 ◽  
Vol 215 ◽  
pp. 193-210 ◽  
Author(s):  
Christian Carloni ◽  
Gianluca Cusatis ◽  
Marco Salviato ◽  
Jia-Liang Le ◽  
Christian G. Hoover ◽  
...  
Keyword(s):  
Size Effect ◽  
Boundary Effect ◽  
Cohesive Crack ◽  
Crack Model ◽  
Cohesive Crack Model ◽  
Critical Comparison ◽  
Effect Model

Scaling Of Fracture In Quasibrittle Materials And The Question Of Possible Influence Of Fractal Morphology

1995 ◽  
Vol 409 ◽  
Author(s):  
Zdeněk P. Bažant
Keyword(s):  
Size Effect ◽  
Asymptotic Expansions ◽  
Asymptotic Properties ◽  
Fractal Nature ◽  
Nonlinear Fracture Mechanics ◽  
Quasibrittle Materials ◽  
Large Size ◽  
Nonlinear Fracture ◽  
Nominal Strength ◽  
Asymptotic Matching

AbstractThe paper presents a review of recent results on the problem of size effect (or the scaling problem) in nonlinear fracture mechanics of quasibrittle materials and on the validity or recent claims that the observed size effect may be caused by the fractal nature of crack surfaces. The problem of scaling is approached through dimensional analysis and asymptotic matching. Large-size and small-size asymptotic expansions of the size effect on the nominal strength of structures are presented, considering not only specimens with large notches (or traction-free cracks) but also structures with no notches. Simple size effect formulas matching the required asymptotic properties are given. Regarding the fractal nature of crack surfaces, it is concluded that it cannot be the cause of the observed size effect.

Scaling of Strength of Metal-Composite Joints—Part III: Numerical Simulation

2013 ◽  
Vol 80 (5) ◽  
Author(s):  
Qiang Yu ◽  
Zdeněk P. Bažant ◽  
Jia-Liang Le
Keyword(s):  
Size Effect ◽  
Fracture Energy ◽  
Peak Load ◽  
Adhesive Layer ◽  
Cohesive Crack ◽  
Crack Model ◽  
Mixed Mode Fracture ◽  
Stress Profile ◽  
Metal Composite ◽  
Cohesive Stress

The size effect in the failure of a hybrid adhesive joint of a metal with a fiber-polymer composite, which has been experimentally demonstrated and analytically formulated in preceding two papers, is here investigated numerically. Cohesive finite elements with a mixed-mode fracture criterion are adopted to model the adhesive layer in the metal-composite interface. A linear traction-separation softening law is assumed to describe the damage evolution at debonding in the adhesive layer. The results of simulations agree with the previously measured load-displacement curves of geometrically similar hybrid joints of various sizes, with the size ratio of 1:4:12. The effective size of the fracture process zone is identified from the numerically simulated cohesive stress profile at the peak load. The fracture energy previously identified analytically by fitting the experimentally observed size effect curves agrees well with the fracture energy of the cohesive crack model obtained numerically by optimal fitting of the test data.

scholarly journals Scaling of Structural Failure

1997 ◽  
Vol 50 (10) ◽  
pp. 593-627 ◽  
Author(s):  
Zdeneˇk P. Bazˇant ◽  
Er-Ping Chen
Keyword(s):  
Size Effect ◽  
Process Zone ◽  
Material Behavior ◽  
Constitutive Law ◽  
Cohesive Crack ◽  
Crack Model ◽  
Rate Dependent ◽  
Quasibrittle Materials ◽  
History Of ◽  
Material Fracture

This article attempts to review the progress achieved in the understanding of scaling and size effect in the failure of structures. Particular emphasis is placed on quasibrittle materials for which the size effect is important and complicated. After reflections on the long history of size effect studies, attention is focused on three main types of size effects, namely the statistical size effect due to randomness of strength, the energy release size effect, and the possible size effect due to fractality of fracture or microcracks. Definitive conclusions on the applicability of these theories are drawn. Subsequently, the article discusses the application of the known size effect law for the measurement of material fracture properties, and the modeling of the size effect by the cohesive crack model, nonlocal finite element models and discrete element models. Extensions to compression failure and to the rate-dependent material behavior are also outlined. The damage constitutive law needed for describing a microcracked material in the fracture process zone is discussed. Various applications to quasibrittle materials, including concrete, sea ice, fiber composites, rocks and ceramics are presented. There are 377 references included in this article.

Sign in / Sign up

Export Citation Format

Share Document