Mode II fracture testing method for highly orthotropic materials like wood

In this paper a mode II fracture testing method has been developed for wood from analytical, experimental and numerical investigations. Analytical results obtained by other researchers showed that the specimen geometry and loading type used for the proposed mode II testing method results in only mode II stress intensity and no mode I stress intensity at the crack tip. Experiments have been carried out to determine mode II fracture toughness K _IIC and fracture energy G _IIF from the test data collected from both spruce (pice abies) and poplar (populus nigra) specimens. It was found that there existed a very good relation between fracture toughness K_IIC and fracture energy G _IIF when the influence of orthotropic stiffness E _II ^* in mode II was taken into account. It verified that for this mode II testing method the formula of LEFM can be employed for calculating mode II fracture toughness even for highly orthotropic materials like wood. In the numerical studies for the tested spruce specimen, the crack propagation process, stress and strain fields in front of crack tips and the stress distributions along the ligament have been investigated in detail. It can be seen that the simulated crack propagating process along the ligament is a typical shear cracking pattern and the development of cracks along the ligament is due to shear stress concentrations at the crack tips of the specimen. It has been shown that this mode II fracture testing method is suitable for measuring mode II fracture toughness K _IIC for highly orthotropic materials like wood.     

A proposed specimen for KIIC testing

Unlike mode I, mode II fracture toughness (K_IIC) testing is still some way from standardization. In the present study, a specimen is proposed for K_IIC testing. The specimen is an adaptation of Richard's (1981) specimen, with the exception that the ligament is extended. Based on numerical analysis, the suitability of the proposed specimen has been assessed by comparing it against the two commonly-used mode II specimens of Banks-Sills and Arcan (1986), and Richard (1981), respectively. In comparison, the proposed specimen has been found to be more compact, and to have a significantly lower intensity of normal stress ahead of the crack tip. As a result, it may be inferred that the proposed specimen would be more suitable for K_IIC testing. The modes I and II K-calibration formulae of the proposed specimen have also been deduced.     

A mode II fracture specimen—finite element analysis

A series of studies which demonstrate the potential of a proposed mode II fracture specimen are reported. First, previously obtained photoelastic results[1–3] are reviewed so that this paper will be self-contained. Then, a finite element analysis is presented in order not only to corroborate the experimental results but also to calibrate the specimen for $\text{K}{}_{\mathrm{IIC}}$ measurements. Finally, a preliminary $\text{K}{}_{\mathrm{IIC}}$ test performed on a brittle steel specimen is described.     

An experimental investigation of the biaxial strength of IM6/3501-6 carbon/epoxy cross-ply laminates using cruciform specimens

Several variations of a thickness-tapered cruciform specimen have previously been used to experimentally determine the biaxial strength of an AS4/3501-6 carbon/epoxy cross-ply laminate. The present work represents a follow-up study of the original specimen design, and incorporates numerous specimen improvements made in an attempt to generate more accurate biaxial results. A total of 52 tests were performed at numerous biaxial stress ratios, utilizing six different specimen configurations. The experimental data generated in the present study for all specimen geometries, as well as a complete biaxial failure envelope in σ₁–σ₂ stress space for this laminate configuration, are presented. A desirable failure mode in the gage section of the specimen was achieved for all specimens tested in the present study, indicating that accurate biaxial stress states were being generated at ultimate specimen failure. The ability of the thickness-tapered cruciform specimen to determine the biaxial strength of composite materials at any stress ratio has been demonstrated.     

Experimental Evaluation of Mixed Mode Stress Intensity Factor for Prediction of Crack Growth by Phoelastic Method

Determination of stress intensity factors K _I, K _II, and constant stress term, σ _ox is investigated. A theory of determining the stress intensity factors using photo-elastic method is formulated taking three stress terms. Three-parameter method of fracture analysis for determining the mixed mode stress intensity factors under biaxial loading conditions from photo-elastic isochromatic fringe data is used. A special biaxial test rig is designed and fabricated for loading the specimen biaxially. A simplified and accurate method is proposed to collect the data from isochromatic fringes. Taking specimen geometry and boundary conditions into account, regression models are developed for estimation of fracture parameters.     

A simple method for the photoelastic determination of mode I stress intensity factors

A new simple method for the photoelastic determination of Mode I stress intensity factors from isochromatics is proposed. This method takes into account the fact that a considerable part of the error committed in the photoelastic determination of Mode I stress intensity factors K_I at crack tips, based on experimentally obtained isochromatic fringe patterns, is due to ignoring the non-singular part of the stress field near the crack tips for the evaluation of these factors. This error can, in most cases, be minimized by an appropriate selection of the polar direction from the crack tip on which the experimental measurements for the subsequent evaluation of the stress intensity factors K_I are made. The suitable polar direction for determining K_I depends in general on the distance of the point where measurements on the isochromatics are made from the crack tip. The method was applied to the problem of a simple crack inside an infinite medium under uniaxial and biaxial loading. A comparison of the present method whith the employed analogous methods shows the superiority of the proposed method.     

A mixed mode fracture specimen for mode II dominant deformation

Several theories have been proposed for the failure of metals, as well as for the angle of crack propagation in mixed mode loading. In order to demonstrate the validity of these theories, the majority of tests have been carried out with an oblique crack placed in a uniaxial stress field. Better testing conditions may be achieved by placing a crack in a uniform bidimensional stress field. A specimen which was recently developed for $\text{K}{}_{\mathrm{IIC}}$ measurement may be readily adapted to achieve a bidimensional stress field and be used for mixed mode testing for the case in which shear deformation is dominant. The main aims of this study are to examine both the cracked and uncracked specimen by means of photoelasticity and finite elements in order to analyze the capabilities and limitations of this specimen for mixed mode testing. It will be demonstrated that there exists a nearly uniform biaxial field in the uncracked specimen. Moreover, calibration formulas will be presented for $\text{K}{}_{\mathrm{I}}$ and $\text{K}{}_{\mathrm{II}}$.     

Experimental study on anchored bars in R.C. elements with transverse reinforcement

In the present paper, the experimental results of pullout tests on anchorages are presented. The experiments allow for the evaluation of bar-to-concrete slip and splitting crack openings at several points along the anchored bar. Particular attention is devoted to the confining contribution of both transverse reinforcement and concrete cover. Two series of tests have been performed: in the first series, the influence of the confining contribution of transverse bars is studied, while in the second series the confining contribution of the concrete cover is analyzed. In specimens from the first series without transverse reinforcement, a splitting collapse of the anchorage occurred at the onset of the slip at the unloaded end of the anchored bar. The opposite was true for all the other specimens, as the transverse reinforcement percentage was such that a pull-out failure of the anchorage occurred. As the stirrup index of confinement Ω rose, the resultant ultimate bond stress value $\bar \tau $ increased; however, beyond the value Ω_max ≈ 0.05, there was no further significant increase of bond strength. The splitting-crack propagation rate exhibited a bilinear trend, with a faster crack propagation when the load was larger than 50% of the peak load.     

The effect of mean stress on delay in fatigue crack growth under load stepdown

The effect of mean stress together with decreasing stress range on fatigue crack propagation behaviour in mild steel is investigated. The delay period between crack arrest and reprogation is found to be a function of the maximum stress intensity factor stepdown ration, K_2max/K_1max. Delay only occurs when this ratio is less than unity. For specimen thicknesses of 1.6 to 6.4 mm, non-propagating cracks, where the affected delay cycles are 500 000 cycles or greater, appear to occur when K_2max/K_1max has a value of approximately 0.7 and the stepdown plastic zone size is about half the initial load plastic zone size, which is approximately equal to the affected crack length.     

Enhancement of mechanical strength by shape memory effect in TiNi fiber-reinforced composites

Since there are strong demands for materials that have the high mechanical properties, the authors developed the new design concept that improve the material strength. It uses SMA to actively control the material strength. Using the TiNi shape memory fiber-reinforced epoxy matrix composite as the test specimen, the experiment was conducted to analyze the effectiveness of the new design concept. The test was conducted by the photoelastic method. The photoelastic fringe patterns and the behavior of K-value at the crack tip clearly support the effectiveness of the new design concept. Then, an analytical model based on Eshelby’s model is developed in order to compute the average matrix compressive stress. The experimental trend that |ΔK₁| increases with prestrain ϵ_T was in good agreement with the predictions based on the present model.     

Experimental research on the compressive fracture toughness of wing fracture of frozen soil

It is commonly found that not only bending fracture but also compressive fracture occur frequently in compression, furthermore, in some specific conditions, compressive fracture sometimes has dominant effect on frozen soil. Therefore, it is extremely necessary to study the mechanical characteristics of the compressive fracture of frozen soil and to investigate the damage and fracture mechanism of frozen soil based on the previous research on frozen soil damage in compression. This study draws on the ideas and methods used in compression fracture research on ice that is very similar to frozen soil, and specific clay in Shenyang region was adopted as the experimental material, to make compressive specimens containing tilted wing crack of different angles, and uniaxial unconfined compression fracture experiments were conducted at different temperatures and loading rates. The fracture toughness K_IC and K_IIC of the main crack tip of the specimens are calculated with obtained experimental results and the law of K_IC and K_IIC changing with tilted angles, temperatures and loading rate is obtained to gain an insight to damage mechanism of frozen soil in compression. This paper presents a meaningful attempt for the research on compressive fracture of frozen soil, so as to better solve practical engineering problems.     

Photoelastic analysis of practical mode I fracture test specimens

A photoelastic technique for the evaluation of the isochromatic fringe patterns of practical Mode I fracture test specimen is presented.The new procedure uncouples the expressions for the stress intensity factor $\text{K}$ and the non-singular stress term $\text{A}$ from the governing maximum shear expression by employing a line perpendicular to the crack-tip in a photoelastic specimen, (this line intersects the isochromatic fringes at the locus of points $\text{r}{}_{\mathrm{i}}$, $\text{θ}{}_{\mathrm{i}}\text{= π/2}$, $\text{i = 1,2,…, n}$, where $\text{n}$ is the maximum analizable fringe) in developing the least-squares technique employed in this research.The least-squares expressions developed required no assumption of initial values for the stress intensity factor $\text{K}$ and the non-singular stress term $\text{A}$. The accuracy of the approach is then demonstrated by obtaining the $\text{K}$ and $\text{A}$ values of some practical Mode I specimens under applied uniaxial and biaxial stresses.     

A photoelastic determination of Ki stress intensity factors

The quantitative relation between the exact solution of the stress field at the vicinity of a crack tip derived fron Westergaard's formulation and the well-known Irwin singular solution was established and results obtained were correlated with photoelastic data for the study of the reigon near the crack tip. The maximum shear stress distribution expressed by the isochromatic pattern for the exact and the singular solution were calculated respectively for uniaxial and biaxial tension. The region where accurate measurements in the isochromatic pattern are possible to evaluate the stress intensity factor to any desired decree of accuracy was established and the extrapolation law for the analysis of the region near the crack tip from data obtained fron the far-field of isochromatics was demonstrated. Experimental evidence corroborated this technique. The method was compared with other already existing experimental methods for the determination of K_I.     

Crack initiation in brittle solids under multiaxial compression

Experiments combined with numerical simulations were used to study crack initiation in brittle materials under biaxial static compression with particular attention to the frictional resistance of the cracks. A new methodology has been developed to prepare specimens with a central crack where crack surfaces are in contact and with the desired friction coefficient: two pieces of Homalite-100 (a brittle polymer) were bonded except for a central region that served as a crack. The measured failure load for cracks with different orientation angles and surface roughness was in close agreement with theoretical predictions for compressive failure. In situ photoelastic fringes were obtained and compared with numerical results enabling the determination of stress distribution along crack faces, as well as the identification of slip and stick regions.     

Constitutive parameters for earthquake rupture dynamics based on high-velocity friction tests with variable sliprate

To reproduce the dynamic rupture process of earthquakes, the fault geometry, initial stress distribution and a frictional constitutive law on the fault are important parameters as initial and boundary conditions of the system. Here, we focus on the frictional constitutive relation on the fault. During a high-speed rupture, fault strength decreases as slip develops which can be described by a slip weakening equation. To understand the physical process of stress breakdown during the dynamic rupture of earthquakes, we investigated the friction behavior of rocks in the laboratory by direct measurements of traction evolution with slip in response to a given slip history. We employed a high-speed rotary shear apparatus introduced at National Research Institute for Earth Science and Disaster Prevention (NIED). This apparatus has a capability of sliding with predefined variable velocities using a servo-controlled system. We used a pair of granite cylindrical specimens with a diameter of 25 mm. As an input signal, we used a regularized Yoffe function to investigate the scale dependence of fracture energy and slip weakening distance (D _c). We observed a positive correlation between D _c and total slip, keeping the maximum slip velocity constant. These conditions correspond to those for earthquakes with the same stress drop and varying magnitudes. Finally, we used a real fault motion; a fault parallel velocity seismogram observed at PS10, 3 km away from the surface fault trace and above the high slip region during the 2002 Denali, Alaska, earthquake. We compared the seismological fracture energy with the corresponding D _c. The relation is linear with an inflection point at D _c = 0.2 m, where the gradient changes. Another interesting feature is that the maximum value of D _c is about 4m even if the total slip exceeds 12 m.     

Influence of bending rotations on three and four-point bend end notched flexure tests

It has been experimentally observed that mode II critical energy release rate (G_IIC) values determined by four-point end notched flexure test and three-point end notched flexure test are different for the same material. At the present work correction factors related to bending rotations are introduced to explain the differences between values of G_IIC obtained by three point and four point end notched flexure tests. The bending angle leads to the contact zones between specimen and supports and specimen and load rollers changing in both test configurations. The present analysis has been carried out by the classical beam theory, neglecting shear effects and assuming the hypothesis of small rotated angles. Results show that the relative differences between corrected and uncorrected values of G_IIC are greater in the case of four-point end notched flexure than in the case of three-point end notched flexure test.     

Mode II interlaminar fracture properties of Moso bamboo

Bamboo is a kind of biological composites reinforced by unidirectional long fiber. Once there exists crack, the propagation of delamination is controlled by the interlaminar fracture toughness instead of by strength. In this paper, the end notched flexure (ENF) beam specimen was used to test the Mode II interlaminar fracture toughness G_IIC along grain of Moso bamboo internode and the fracture surface was analyzed. The results were obtained that the Mode II interlaminar fracture toughness G_IIC calculated by the experiment parameter substitution method was more accurate and the value was 1303.18 J/m² (coefficient of variation = 8.96%) which was about three times higher than the value of Mode I interlaminar fracture toughness; the crack propagation of Mode II interlaminar fracture was mainly self-similar cracking, but the fracture surface was rougher. Ground tissue in the zone of Mode II crack propagation was characterized by hackle shearing deformation. The SEM photos showed that ground tissue separated from fiber along middle lamella under shear stress and as the increasing of the dislocation of upper and lower layer, the thin-walled ground tissue would fracture transversely by tension, while to thick-walled fiber cell, only middle lamella and primary wall were torn then debonded, fragments remained.     

An investigation of the edge-sliding mode in fracture mechanics

A boundary collocation procedure has been applied to the Williams stress function to determine the elastic stress distribution for the crack tip region of a finite, edge-cracked plate subjected to mode II loading at the crack tips. The asymmetric specimen selected was particularly suitable for the determination of plane strain fracture toughness for mode II loading. Numerical solutions for stress intensity factors for the edge-sliding mode obtained by the boundary collocation method were in close agreement with values obtained from photoelastic experiments.Fracture tests of several compact shear specimens of 2024-T4 aluminum were conducted in order to experimentally investigate the behavior of the edge-sliding mode. In each case a brittle shear failure was observed and mode II fracture toughness values were obtained. The average value for K_IIc obtained from two tests was 39.5 ksi(in)^{$\text{1}\text{2}$}. No K_Ic. data for 2024-T4 were available for comparison purposes; however, K_Ic values for a similar alloy, 2024-T351, have been reported as 34ksi(in)^{$\text{1}\text{2}$} which is only about 15 per cent below the corresponding K_IIc value.     

On fatigue lives of diecast and extruded Mg alloys

In this study, fatigue tests were carried out on both diecast and extruded Mg alloys to study their distributions of fatigue lives under constant stress amplitudes. During the fatigue process of the diecast Mg alloy, cracks initiated from the casting defects inside of the specimen, and then propagated prior to final failure of the specimen. While in the extruded Mg alloy, cracks initiated from the inclusions located on the specimen surface. With assuming the above defects as the initial cracks, the initial maximum stress intensity factors K_imax were evaluated. There are common relations between the initial maximum stress intensity factors K_imax and fatigue lives N_f, regardless of the stress amplitudes for the both Mg alloys at the constant R ratio of −1. The lower K_imax, the longer N_f becomes. Integrating the fatigue crack propagation law from the initial maximum stress intensity factor K_imax to the fatigue fracture toughness K_fc, the relations K_imax vs. N_f can be successfully evaluated.Distributions of fatigue lives at the constant stress amplitudes can be represented by the Weibull distributions. Dispersion in the fatigue lives becomes larger at the lower stress amplitude as compared with those at the higher stress amplitudes. This trend is observed commonly for both diecast and extruded Mg alloys.