Fracture toughness of autoclaved aerated concrete

So far, few experiments to determine fracture toughness of autoclaved aerated concrete have been reported in the literature. Tests on three different types of autoclaved aerated concrete using six different specimen geometries have been carried out. Four of the six specimen geometries chosen lead to nearly identical results for K_IC. The two other types of specimen were used to determine fracture energy G_f. K_IC increases with compressive strength of the material. Fracture energy is about one tenth of the corresponding value of normal concrete. The influence of rate of loading on K_IC can be expressed by means of a power law. These results suggest that linear elastic fracture mechanics is a suitable approximation for the calculation of crack propagation in autoclaved aerated concrete.     

Effect of notch width on KIC for mortar and concrete

Test were carried out on mortar and concrete to determine whether the fracture toughness depends upon the length of the crack front. Notched beams were prepared with a constant length of 203.2 mm and depth of 50.8 mm, but with the width (length of crack front) varying from 45 to 254 mm. They were tested in 3-point bending to obtain K_IC. It was found that within the range studied there is no dependence of fracture toughness upon the length of the crack front. The fracture toughness test described in ASTM E399-74 for metals appeared to be adequate for concrete also.     

Fracture behavior of poled piezoelectric PZT under mechanical and electrical loads

Four point bending samples were poled parallel to the long axis, notched and fractured. During mechanical loading, a constant electric field was applied parallel or antiparallel to the poling direction (perpendicular to the crack surface). Assuming electrical crack boundary conditions of (i) an impermeable or (ii) a completely permeable crack, the stress intensity factors K_I and the field intensity factors K_IV at failure were determined by linear-piezoelectric finite element calculations. The fracture curve K_IC(K_IV) for the impermeable crack model does not comply to fracture criteria based on the total energy release rate or on the mechanical energy release rate. Within the completely permeable crack model, it appears generally impossible to describe electric field effects on the fracture resistance. Some theoretical extensions of the crack models are discussed which might contribute to resolve the aforementioned problems.     

Notch sensitivity of concrete and size effect part II: Stress state effect

The problem of notch sensitivity of concrete is discussed with the influence of size effect being taken into account. The need to consider the size effect on the tensile strength of concrete was noted. The simple dependence of the critical stress intensity factor K_IC on stress state, specimen and crack geometry, tensile strength and structure of material is found. When analysing the fictitious crack model the fracture zone length is calculated as a function of specimen and crack geometry and structure of the material. The directions of further research are discussed.     

Fracture toughness of particle filled fiber reinforced polyester composites

Fracture behavior of polyester composite systems, polyester mortar and glass fiber reinforced polyester mortar, was investigated in mode I fracture using single edge notched beams with varying notch depth. The beams were loaded in four-point bending. Influence of polymer content on the flexural and fracture behavior of polyester composites at room temperature was studied using a uniform Ottawa 20–30 sand. The polymer content was varied between 10 and 18% of the total weight of the composite. The flexural strength of the polyester mortar systems increase with increase in polymer content while the flexural modulus goes through a maximum. The critical stress intensity factor (K_IC) for the optimum polyester mortar (14%) was determined by two methods including a method based on crack mouth opening displacement. The K_IC for polyester mortar is linearly related to the flexural strength. Polyester mortar (18%) reinforced with 4% glass fibers was also investigated, and crack growth resistance curve (K_R) was developed with crack extension (Δa). A model has been proposed to represent the fracture toughness with change in crack length, K_R - Δa relationship, of fiber reinforced polyester composite.     

Crack propagation in silica from reactive classical molecular dynamics simulations

Mechanistic insight into the process of crack growth can be obtained through molecular dynamics (MD) simulations. In this investigation of fracture propagation, a slit crack was introduced into an atomistic amorphous silica model and mode I stress was applied through far‐field loading until the crack propagates. Atomic displacements and forces and an Irving–Kirkwood method with a Lagrangian kernel estimator were used to calculate the J‐integral of classical fracture mechanics around the crack tip. The resulting fracture toughness (K_IC), 0.76 ± 0.16 MPa√m, agrees with experimental values. In addition, the stress fields and dissipation energies around the slit crack indicate the development of an inelastic region ~30Å in diameter. This is one of the first reports of K_IC values obtained from up‐scaled atomic‐level energies and stresses through the J‐integral. The application of the ReaxFF classical MD force field in this study provides the basis for future research into crack growth in multicomponent oxides in a variety of environmental conditions.     

Mixed-mode fracture behavior of glass fiber reinforced polymer concrete

Fracture toughness of chopped strand glass fiber reinforced particle-filled polymer composite beams was investigated in Mode I and Mode III loading conditions using three-point bend tests. Effects of crack angles on fracture behavior were also studied. The specimens, which have inclined crack at an angle θ to the axis of the specimens, were used to carry out the tests. The specimens were tested with inclination angles 30°, 45°, 60° and 75°. The results are compared with the values of K_IC obtained using conventional (θ=90° ) specimens. In addition, J integrals were also determined. J_IC increases continuously with increasing in crack angle from θ=30° to θ=90°. In contrast, J_IIIC decreases with the crack inclination angle θ from 30° to 90°.     

Fracture characteristics of concrete at early ages

The purpose of this study is to experimentally investigate, at early ages, the fracture characteristics of concrete such as critical crack tip opening displacement, critical stress intensity factor, fracture energy, and bilinear softening curve based on the concepts of the effective-elastic crack model and the cohesive crack model.A wedge-splitting test for Mode I was performed on cubical specimens with an initial notch at the edge. By taking various strengths and ages, load-crack mouth opening displacement (CMOD) curves were obtained and these curves were evaluated by linear elastic fracture mechanics and finite element analysis.The results from the test and analysis indicate that critical crack tip opening displacement decreases and critical stress intensity factor and fracture energy increase with concrete ages from Day 1 to Day 28. By numerical analysis, four parameters of bilinear softening curves from Day 1 to Day 28 were obtained. In addition, it was observed that the parameters f_t and f₁ increase and the parameters w₁ and w_c decrease with increasing age. The obtained fracture parameters and bilinear softening curves at early ages may be used as a fracture criterion and an input data for finite element analysis of concrete at early ages.     

Additive effect of micro-damage zones from nano-scale crack tip and nano-grains for fracture toughness measurements of 3Y-TZP zirconia ceramics

A nano-scale crack tip around 500 nm wide introduced by femtosecond laser still affects the accuracy of fracture toughness K_IC measurements of 3Y-TZP zirconia ceramics with average grain size G from 200 to 500 nm. A simple formula was proposed to estimate the additive effect of crack-tip damage zones from an infinitely sharp crack to a nano-scale blunt notch. The error in fracture toughness measurements is less than 8 % if the nano-scale crack-tip width < 0.5·G. The intrinsic K_IC can be deduced from the simple formula if the nano-scale crack tip > 0.5·G. This study shows the same K_IC was deduced from two different sets of 3Y-TZP measurements with nano- and micro-scale notches of 500 nm and 18 µm wide. Furthermore, the simple formula specifies the relation between the fracture toughness K_IC and intrinsic strength f_t via grain size G, which means K_IC can also be estimated from f_t and G without testing pre-cracked specimens. K_IC values of 3Y-TZP from specimens with and without pre-cracks were compared.     

Influence of graphite on the low-frequency fatigue behavior of zirconium diboride ceramics

The fatigue behavior of a ZrB₂-based ceramic containing SiC and graphite was compared to a ZrB₂-SiC reference material based on bending testing, quantitative calculations as well as crack growth and fracture characterization. The addition of graphite flake makes ZrB₂-SiC-Graphite ceramics exhibit fatigue failure behavior at very high stress level (93% of the characteristic strength, σ₀), owing to the increased K_Ic promoted by crack deflection, bridging, bifurcation and pull-out of graphite, while the fatigue behavior of ZrB₂-SiC appears when the maximum stress is below ~86%σ₀. However, both the slow crack growth exponents of the graphite containing ceramic, n and nc values, which reflect the fatigue resistance in static and cyclic fatigue conditions, respectively, are only 1/4 as compared to the reference graphite-free ceramic. This may be due to the weak boride/graphite interfaces, which lead to the decrease of the initial critical stress intensity factor (K_c-initial) value from 2.6 to 2.0 MPa m^1/2.     

Fatigue crack growth behavior and mechanism of closed‐cell PVC foam

The applicability of linear‐elastic fracture mechanics parameters (ΔK and K_max), elastic–plastic fracture mechanics parameter (ΔJ), and time‐dependent fracture mechanics parameter (C*) to characterize fatigue crack growth (FCG) rate of closed‐cell polyvinyl chloride foam was investigated in the present work. The effect of stress ratios (R = 0.1 and 0.4) on FCGs was observed when the ΔK, K_max and ΔJ were used as fracture mechanics parameters. As a fracture mechanics parameter that combines ΔK and K_max, the K* successfully characterized FCGs (da/dN) at R = 0.1 and 0.4. While, a time‐dependent fracture mechanics parameter (C*) successfully correlated da/dt of creep crack growth (CCG) test, but it failed to correlate da/dt of FCG tests. The FCGs at both R = 0.1 and 0.4 were cyclic dependent, while the CCG was time dependent. For cyclic‐dependent crack growth, the interaction between polymer‐chain scission and small scale crack‐tip blunting was the main mechanism, whereas the interaction between polymer‐chain pullout and large scale crack‐tip blunting dominated fracture process for time‐dependent crack growth. POLYM. ENG. SCI., 2013. © 2012 Society of Plastics Engineers     

A reinvestigation of the validity of the indentation fracture (IF) method as applied to ceramics

Poor correlation between indentation fracture resistance, K_IFR, and fracture toughness, K_IC, has long been considered a weak point of the indentation fracture (IF) method of materials analysis. The present work therefore assessed the reliability of the experimental data that has historically been used for comparisons of K_IFR and K_IC. A painstaking survey of primary literature reports concerning the IF method revealed that the comparisons of K_IC with K_IFR in most studies were imperfect because both K_IC and K_IFR were measured using unreliable techniques and because improper test materials such as silicate glass were employed. These findings indicate that the standard objections against the use of the IF model are not well supported, and also that the majority of the empirically-derived calibration constants used in various IF equations are suspect. Accordingly, it is evident that new experimental measurements using the latest and most reliable techniques will be required to allow well-informed discussions of the validity of this test method in future.     

Evaluation of the thermal shock fracture toughness of reactor graphites by arc discharge heating

This paper presents a new technique to determine the thermal shock fracture toughness by a basic analysis of stress intensity factors of the disk with an edge crack. The thermal shock fracture toughness is defined as $\text{K}{}_{\mathrm{IC}}\text{k}\text{Eα}$ (K_IC standing for fracture toughness value of the mode I; k for thermal conductivity; E for Young's modulus; α for thermal expansion coefficient) and is determined en bloc by measuring the threshold electric power of the arc discharge heating produced when an edge crack propagates in the disk. This is intimately corelated to the thermal shock resistance presented previously. Experimental data for four kinds of reactor graphite are shown.     

Assessing fracture toughness in sintered Al2O3–ZrO2(3Y)–SiC ceramic composites through indentation technique

Al₂O₃–ZrO₂(3Y)–SiC ceramic composites were prepared by spark plasma sintering. The fracture toughness (K_1C) of the material was evaluated by indentation technique using different types of empirical formulas between 29.4 N and 98 N. The calculated K_1C values depend on the crack profile and the applied load. By analyzing the relationship between the indentation radius and the crack length and the crack profile, the crack form of the composite is determined as a Palmqvist crack. Raman spectra result shows that ZrO₂ has a significant martensitic phase transformation when the applied load is 5 kg or higher. Additionally, the K_1C value decreases slightly as the load increases. The equation based on the Palmqvist crack system and the curve fitting equation are more suitable for the calculation of the K_1C value of the material. The composite exhibits a combination of various toughening mechanisms, such as crack deflection and bridging, thereby improving the fracture toughness of the material.     

Time and temperature effects on the fracture toughness of rigid poly(vinylchloride) pipe materials

The fracture toughness of rigid poly(vinylchloride) pipe materials has been investigated over a range of temperatures and rates. Conditions are described for valid fracture toughness (K_IC) tests and notch insensitive (ductile) behavior; time-temperature effects on transitions in K_IC are defined. The modes of crack extension are characterized over a range of temperatures, and the mechanisms of crack resistance are discussed, including some quantitative data for the yielded zone at the crack tip.     

Toughening epoxies with halloysite nanotubes

An experimental attempt was made to characterize the fracture behaviour of epoxies modified by halloysite nanotubes and to investigate toughening mechanisms with nanoparticles other than carbon nanotubes (CNTs) and montmorillonite particles (MMTs). Halloysite-epoxy nanocomposites were prepared by mixing epoxy resin with halloysite particles (5 wt% and 10 wt%, respectively). It was found that halloysite nanoparticles, mainly nanotubes, are effective additives in increasing the fracture toughness of epoxy resins without sacrificing other properties such as strength, modulus and glass transition temperature. Indeed, there were also noticeable enhancements in strength and modulus for halloysite-epoxy nanocomposites because of the reinforcing effect of the halloysite nanotubes due to their large aspect ratios. Fracture toughness of the halloysite particle modified epoxies was markedly increased with the greatest improvement up to 50% in K_IC and 127% in G_IC. Increases in fracture toughness are mainly due to mechanisms such as crack bridging, crack deflection and plastic deformation of the epoxy around the halloysite particle clusters. Halloysite particle clusters can interact with cracks at the crack front, resisting the advance of the crack and resulting in an increase in fracture toughness.     

Peak stress intensity dictates fatigue crack propagation in UHMWPE

The majority of total joint replacements employs ultra-high molecular weight polyethylene (UHMWPE) for one of the bearing components. These bearings may fail due to the stresses generated in the joint during use, and fatigue failure of the device may occur due to extended or repeated loading of the implant. One method of analysis for fatigue failure is the application of fracture mechanics to predict the growth of cracks in the component. Traditional analyses use the linear elastic stress intensity factor K to describe the stresses near a loaded crack. For many materials, such as metals, it is the range of stress intensity, ΔK, that determines the rate of crack propagation for fatigue analysis. This work shows that crack propagation in UHMWPE correlates to the maximum stress intensity, K_max, experienced during cyclic loading. This K_max dependence is expected due to the viscoelastic nature of the material and the absence of crazing or other cyclic load dependent crack tip phenomena. Such a dependence on a non-cyclic component of the stress allows cracks to propagate under load with little or no fluctuating stresses. Consequently, traditional fatigue analyses, which depend on the range of the stress to predict failure, are not always accurate for this material. For example, significant static stresses that develop near stress concentrations in the component locking mechanisms of orthopedic implants make such locations likely candidates for premature failure due the inherent underestimate of crack growth obtained from conventional fatigue analyses.     

Mechanical properties of BaCe0.65Zr0.2Y0.15O3-δ – Ce0.85Gd0.15O2-δ dual-phase proton-conducting material with emphasis on micro-pillar splitting

BaCe_0.65Zr_0.2Y_0.15O_3-δ – Ce_0.85Gd_0.15O_2-δ (BCZ20Y15-GDC15) dual-phase material revealed potential for H₂ production technologies due to its exceptional H₂ permeation and chemical resistance. In this article, mechanical properties of BCZ20Y15-GDC15 dual-phase material were investigated to evaluate the mechanical behavior and develop strategies to warrant structural stability. Elastic modulus, hardness and fracture toughness values were studied using different indentation-based methods. The fracture experiments at different length-scales both revealed that the introduction of GDC15 makes the material tougher, facilitating the further design of robust and reliable components.     

Critical stress intensity factor of epoxy mortar

Fracture behavior of epoxy mortar was investigated in Mode I fracture using single edge notched beams with varying notch depth and beam thickness. The beams were loaded in both 3-point and 4-point bending. Influence of polymer content and temperature on the fracture behavior of epoxy mortar was studied using uniform Ottawa 20–30 sand. The polymer content was varied between 10 percent and 18 percent of the total weight of the composite. The temperature was varied between 22°C and 120°C. The flexural strength of the polymer mortar increases with increase in polymer content while the flexural modulus goes through a maximum. The critical stress intensity factor (K_IC) was determined by several methods including compliance method (based on crack mouth opening displacement) and finite element analysis. The K_IC for epoxy mortar increases with increase in polymer content and epoxy mortar strength but decreases with increase in temperature. The critical stress intensity factor of epoxy mortar is represented in terms of polymer content and polymer strength or stiffness. Numerical tests based on random sampling and stratified sampling procedures were performed to substantiate the experimentally observed fracture toughness values of epoxy mortar.