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 Laws and Multiscale Approach in the Mechanics of Heterogeneous and Disordered Materials

2006 ◽  
Vol 59 (5) ◽  
pp. 283-305 ◽  
Author(s):  
Alberto Carpinteri ◽  
Pietro Cornetti ◽  
Simone Puzzi
Keyword(s):  
Tensile Strength ◽  
Fracture Energy ◽  
Scaling Laws ◽  
Scale Effects ◽  
Failure Process ◽  
Cohesive Crack ◽  
Disordered Materials ◽  
Multiscale Approach ◽  
Crack Model ◽  
Cohesive Crack Model

The present paper is a review of research carried out on scaling laws and multiscaling approach in the mechanics of heterogeneous and disordered materials in the last two decades, especially at the Politecnio di Torino. The subject encompasses theoretical, numerical and experimental aspects. The research followed two main directions. The first one concerns the implementation and the development of the cohesive crack model, which has been shown to be able to simulate experiments on concrete like materials and structures. It is referred to as the dimensional analysis approach, since it succeeds in capturing the ductile-to-brittle transition by increasing the structural size owing to the different physical dimensions of two material parameters: the tensile strength and the fracture energy. The second research direction aims at capturing the size-scale effects of quasibrittle materials, which show fractal patterns in the failure process. This approach is referred to as the renormalization group (or fractal) approach and leads to a scale-invariant fractal cohesive crack model. This model is able to predict the size effects even in tests where the classical approach fails, e.g., the direct tension test. Within this framework and introducing the fractional calculus, it is shown how the Principle of Virtual Work can be rewritten in its fractional form, thus obtaining a scaling law not only for the tensile strength and the fracture energy, but also for the critical strain.

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

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.

Eigenvalue analysis of size effect for cohesive crack model

1994 ◽  
Vol 66 (3) ◽  
pp. 213-226 ◽  
Author(s):  
Yuan-Neng Li ◽  
Zdeněk P. Bažant
Keyword(s):  
Size Effect ◽  
Cohesive Crack ◽  
Eigenvalue Analysis ◽  
Crack Model ◽  
Cohesive Crack Model

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.

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.

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