Fiber Pullout Characteristics Under Dynamic Loading Conditions

2001 ◽  
Author(s):  
N. Sridhar ◽  
Q. D. Yang ◽  
B. N. Cox
Keyword(s):  
Shear Stress ◽  
Crack Opening ◽  
Interfacial Shear Stress ◽  
Friction Stress ◽  
Crack Plane ◽  
Opening Displacement ◽  
Fiber Pullout ◽  
Dynamic Propagation ◽  
Dependent Relationship ◽  
The Matrix

Abstract Inertial effects in the mechanism of fiber pullout during dynamic propagation of a bridged crack are critically examined. By reposing simple shear lag models of pullout as problems of dynamic wave propagation, the effect of frictional coupling between the fiber and the matrix is accounted for in a fairly straightforward way. The frictional sliding between the fiber and the matrix is described by a constant interfacial friction stress, the sign of which depends on the relative particle velocity of the fiber and the matrix. Analytical solutions are derived when the load or bridging traction on the fiber in the crack plane increases linearly in time. The results show that when the wave speed of the matrix exceeds a critical value, the frictional fiber pullout behavior transitions from a state of pure slip to a state where part of the sliding zone slips and the remaining sticks. When stick occurs, the fiber and the matrix within the stick zone slide past each other with an interfacial shear stress less than the shear stress required for slipping. Regions of slip and stick propagate and increase with time and influence the time-dependent relationship between the crack opening displacement and the bridging tractions.

scholarly journals Mechanics Of Crack Bridging Under Dynamic Loads

2000 ◽  
Vol 653 ◽  
Author(s):  
N. Sridhar ◽  
B.N. Cox ◽  
C.L. Dunn ◽  
I.J. Beyerlein
Keyword(s):  
Crack Opening ◽  
Dynamic Crack Propagation ◽  
Geometrical Parameters ◽  
Dynamic Crack ◽  
Inertial Effects ◽  
Opening Displacement ◽  
Dynamic Propagation ◽  
Dependent Relationship ◽  
Fibre Pullout ◽  
The Matrix

AbstractA bridging law for fiber reinforced composites under dynamic crack propagation conditions has been derived. Inertial effects in the mechanism of fibre pullout during dynamic propagation of a bridged crack are critically examined for the first time. By reposing simple shear lag models of pullout as problems of dynamic wave propagation, the effect of the frictional coupling between the fibres and the matrix is accounted for in a fairly straightforward way. The solutions yield the time-dependent relationship between the crack opening displacement and the bridging traction. Engineering criteria and the role of material and geometrical parameters for significant inertial effects are identified.

Plastic relaxation at a crack tip by asymmetric slip

1988 ◽  
Vol 418 (1854) ◽  
pp. 261-280 ◽  
Keyword(s):  
Slip Band ◽  
Crack Opening ◽  
Crack Tip ◽  
Friction Stress ◽  
Small Scale ◽  
Crack Tip Opening Displacement ◽  
Opening Displacement ◽  
Sharp Crack ◽  
Scale Yielding ◽  
Crack Tip Opening

Relaxation at a sharp crack tip by a single slip band is considered. It is shown that for mixed-mode loading of a plane crack in an isotropic medium there is a unique angle between the slip band and the crack for which the energy release rate (or stress intensity factor) of the crack can be reduced to zero. For such a slip-band calculations are made of the slipband length and the crack-opening displacement as a function of the loading, crack length and friction stress acting on dislocations in the slip band. For small-scale yielding, a simple model is discussed that gives a good approximation to the crack-tip opening displacement and slip-band angle.

Anisotropic Media with a Crack or a Rigid Line Inclusion,

1996 ◽  
Author(s):  
T. T. C. Ting
Keyword(s):  
Crack Opening Displacement ◽  
Crack Opening ◽  
Null Vector ◽  
Opening Displacement ◽  
Rigid Line Inclusion ◽  
Rigid Line ◽  
The Matrix ◽  
Structural Failures ◽  
The Right ◽  
Line Inclusion

A crack, or cracks, in a material is perhaps one of the most studied problems in solid mechanics. This is due to the fact that many structural failures are related to the presence of a crack in the material. The knowledge of stress distribution near a crack tip is indispensable in a fracture mechanics analysis (Rice, 1968; Sih and Liebowitz, 1968; Sih and Chen, 1981; Kanninen and Popelar, 1985; K. C. Wu, 1989a). A crack is represented by a slit cut whose surfaces are assumed traction-free. This is a mathematical idealization. For a composite material that consists of stiff short fibers or whiskers in the matrix, we have rigid line inclusions. A rigid line inclusion is the counterpart of a crack. It is sometimes called an anticrack. The displacement at a rigid line inclusion either vanishes or has a rigid body translation and rotation. One of the puzzling problems for a crack is the one when it is located on the x1-axis that is an interface between two dissimilar materials. The displacement of the crack surfaces near the crack tips may oscillate, creating a physically unacceptable phenomenon of interpenetration of two materials. The bimaterial tensor Š introduced in Section 8.8 plays a key role in the analysis. If Š vanishes identically, there is no oscillation. If Š is nonzero, we may decompose the tractions applied on the crack surfaces into two components, one along the right null vector of Š denoted by to and the other on the right eigenplane of Š denoted by tγ . The solution associated with to is not oscillatory. It has the property that the traction on the interface x2=0 is polarized along the right null vector of Š while the crack opening displacement is polarized along the left null vector of Š. The solution associated with tγ is oscillatory. It has the property that the traction on the interface x2=0 is polarized on the right eigenplane of Š while the crack opening displacement is polarized on the left eigenplane of Š.

Matrix Cracking In Brittle-Matrix Composites with Tailored Interfaces

1994 ◽  
Vol 365 ◽  
Author(s):  
Sawai Danchaivijit ◽  
L-Y. Chao ◽  
D. K. Shetfty
Keyword(s):  
Steady State ◽  
Crack Length ◽  
Uniaxial Tension ◽  
Sliding Friction ◽  
Crack Opening ◽  
State Theory ◽  
Matrix Cracking ◽  
Opening Displacement ◽  
The Matrix ◽  
Cracking Stress

ABSTRACTMatrix cracking from controlled through cracks with bridging filaments was studied in a model unidirectional composite of SiC filaments in an epoxy-bonded alumina matrix. An unbonded, frictional interface was produced by moderating the curing shrinkage of the epoxy with the alumina filler and coating the filaments with a releasing agent. Uniaxial tension test specimens (2.5 × 25 × 125 mm) with filament-bridged through cracks were fabricated by a novel two-step casting technique involving casting, precracking and joining of cracked and uncracked sections. Distinct matrix-cracking stresses, corresponding to the extension of the filamentbridged cracks, were measured in uniaxial tension tests using a high-sensitivity extensometer. The crack-length dependence of the matrix-cracking stress was found to be in good agreement with the prediction of a fracture-mechanics analysis that employed a new crack-closure force - crack-opening displacement relation in the calculation of the stress intensity for fiber-bridged cracks. The prediction was based on independent experimental measurements of the matrix fracture toughness (Kcm), the interfacial sliding friction stress (τ) and the residual stress in the matrix (σmI). The matrix-cracking stress for crack lengths (2a) greater than 3 mm was independent of the crack length and agreed with the prediction of the steady-state theory of Budiansky, Hutchinson and Evans[2]. Tests on specimens without the deliberately introduced cracks indicated a matrix-cracking stress significantly higher than the steady-state stress.

Stress Distribution of the Composites Reinforced by Slub-Like Short Fibers

2007 ◽  
Vol 353-358 ◽  
pp. 389-391 ◽  
Author(s):  
Li Xin Dong ◽  
Guang Ze Dai ◽  
Xian Feng Zhou ◽  
L.L. Liu ◽  
Qing Qing Ni
Keyword(s):  
Shear Stress ◽  
Stress Distribution ◽  
Textile Industry ◽  
Axial Stress ◽  
Interfacial Shear Stress ◽  
Interfacial Shear ◽  
Reinforced Composites ◽  
Stress Distributions ◽  
Short Fibers ◽  
The Matrix

The model of slub-like short fibers reinforced composites is suggested from the viewpoint of bamboo in the nature and patterns characteristic of simulated silk PET used in textile industry. The stress distributions in the enlarged-end fiber and in the matrix are analyzed. The axial stress in the fiber and matrix is found to increase and the interfacial shear stress decrease with the radius of the enlarged end.

scholarly journals Criteria For Progressive Interfacial Debonding With Friction In Fiber-Reinforced Ceramic Composites

1995 ◽  
Vol 409 ◽  
Author(s):  
Chun-Hway Hsueh
Keyword(s):  
Axial Strain ◽  
Crack Opening ◽  
Ceramic Composites ◽  
Interfacial Debonding ◽  
Fiber Reinforced ◽  
Opening Displacement ◽  
Strain Criterion ◽  
Mismatch Strain ◽  
The Matrix ◽  
Debonded Interface

AbstractCriteria for progressive debonding at the fiber/matrix interface with friction along the debonded interface are considered for fiber-reinforced ceramic composites. The energy-based criterion is adopted to analyze the debond length, the crack-opening displacement, and the displacement of the composite due to interfacial debonding. The analytical solutions are identical to those obtained from the mismatch-strain criterion, in which interfacial debonding is assumed to occur when the mismatch in the axial strain between the fiber and the matrix reaches a critical value. Furthermore, the mismatch-strain criterion is found to bear the same physical meaning as the strength-based criterion.

Application of the Shakedown Theory to Brittle-Matrix Fiber-Reinforced Cracked Composite Beams Under Combined Traction and Flexure

2013 ◽  
Vol 81 (3) ◽  
Author(s):  
Andrea Spagnoli ◽  
Andrea Carpinteri ◽  
Lorenzo Montanari
Keyword(s):  
Crack Opening ◽  
Optimization Procedure ◽  
Discrete Problem ◽  
Opening Displacement ◽  
Programming Technique ◽  
Cracking Behavior ◽  
Linear Elastic ◽  
Perfectly Plastic ◽  
Load Paths ◽  
The Matrix

The cracking behavior of a composite beam with multiple reinforcing fibers under periodic traction-flexure is analyzed through a fracture mechanics-based model, where the edge-cracked beam section is exposed to external loads and crack bridging reactions due to the fibers. Assuming a rigid-perfectly plastic bridging law for the fibers and a linear-elastic law for the matrix, the statically indeterminate bridging forces are obtained from compatibility conditions. Under general load paths, shakedown conditions are explored by making use of the Melan's theorem, here reformulated for the discrete problem under consideration, where crack opening displacement at the fiber level plays the role of plastic strain in the counterpart problem of an elastic-plastic solid. The limit of shakedown is determined through an optimization procedure based on a linear programming technique.

Elastic Wave Scattering from an Interface Crack: Antiplane Strain

1987 ◽  
Vol 54 (3) ◽  
pp. 503-508 ◽  
Author(s):  
A. Bostro¨m
Keyword(s):  
Interface Crack ◽  
Crack Opening ◽  
Plane Waves ◽  
Integral Equation Method ◽  
Far Field ◽  
Antiplane Strain ◽  
Opening Displacement ◽  
Direct Integral ◽  
The Matrix ◽  
Scattering Of Elastic Waves

The two-dimensional scalar problem of scattering of elastic waves under antiplane strain from an interface crack between two elastic half-spaces is considered. The method used is a direct integral equation method with the crack-opening displacement as the unknown. Chebyshev polynomials are used as expansion functions and the matrix in the resulting equations is simplified by contour integration techniques. The scattered far field is expressed explicitly in simple functions and the expansion coefficients. The consequences of energy conservation are explored and are used as a check in the numerical implementation. For incoming plane waves numerical results are given for the total scattered energy and the far field amplitude.

scholarly journals Determination of fracture parameters for interface cracks in transverse isotropic magnetoelectroelastic composites

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
Jun Lei ◽  
Pengbo Sun ◽  
Tinh Quoc Bui
Keyword(s):  
Crack Opening ◽  
Crack Plane ◽  
Interfacial Cracks ◽  
Fracture Parameters ◽  
Extrapolation Formula ◽  
Poling Direction ◽  
The Matrix ◽  
Transverse Isotropic ◽  
Crack Faces ◽  
Displacement Extrapolation

AbstractTo determine fracture parameters of interfacial cracks in transverse isotropic magnetoelectroelastic composites, a displacement extrapolation formula was derived. The matrix-form formula can be applicable for both material components with arbitrary poling directions. The corresponding explicit expression of this formula was obtained for each poling direction normal to the crack plane. This displacement extrapolation formula is only related to the boundary quantities of the extended crack opening displacements across crack faces, which is convenient for numerical applications, especially for BEM. Meantime, an alternative extrapolation formula based on the path-independent J-integral and displacement ratios was presented which may be more adaptable for any domain-based numerical techniques like FEM. A numerical example was presented to show the correctness of these formulae.

scholarly journals Effect of a Bio-Based Dispersing Aid (Einar® 101) on PLA-Arbocel® Biocomposites: Evaluation of the Interfacial Shear Stress on the Final Mechanical Properties

Biomolecules ◽  
2020 ◽  
Vol 10 (11) ◽  
pp. 1549
Author(s):  
Laura Aliotta ◽  
Vito Gigante ◽  
Patrizia Cinelli ◽  
Maria-Beatrice Coltelli ◽  
Andrea Lazzeri
Keyword(s):  
Mechanical Properties ◽  
Shear Stress ◽  
Quantitative Estimation ◽  
Interfacial Shear Stress ◽  
Impact Resistance ◽  
Cellulose Fibers ◽  
Interfacial Shear ◽  
Analytical Models ◽  
Poly Lactic Acid ◽  
The Matrix

In this paper, the production and the characterization of poly (lactic) acid (PLA)-based composites containing different amounts (from 10 wt.% to 25 wt.%) of ultra-short cellulose fibers (Arbocel 600 BE/PU) have been investigated. On the basis of a previous study, it was observed that the addition of the cellulose fibers led to an embrittlement of the composite. Consequently, in order to obtain a composite with enhanced impact resistance and elongation at break, the effect of the Einar 101 addition (a bio-based dispersing aid additive) was analyzed. The role of the adhesion between the fiber and the matrix, coupled with a better fiber dispersion, was thus evaluated. Also, the consequences on the final mechanical properties (tensile and impact test) caused by the Einar addition were investigated. Analytical models were also applied in order to obtain an evaluation of the variation of the interfacial shear stress (IFSS) (strictly correlated to the fiber-matrix adhesion) caused by the Einar introduction. Furthermore, due to the very low aspect ratio of the Arbocel fibers, a suitable Bader and Boyer model variation was adopted in order to have a better quantitative estimation of the IFSS value.

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