Classification of stress-intensity factors from isochromatic-fringe patterns

The stresses in the local neighborhood of a crack tip have been used to develop a relation between the isochromatic-fringe orderN, its position parametersr and θ and the stress field expressed in terms of stress intensities,K _I ,K _II , and a far-field stress σ _ox . This relation was programmed and a plotting routine was developed to map isochromatic (σ₁ ? σ₂) fields in the neighborhood of the crack tip. The stress intensitiesK _I andK _II and the far-field stress σ _ox were varied and isochromatic fields were constructed for each combination. As bothK _II and σ _ox influence the size, shape and orientation of the isochromatics loops in a systematic manner, the pictorial representation of the isochromatic fields can be used to classify the state of stress (K _I ,K _II and σ _ox ) at the crack tip. Isochromatics which classify six different states of stress have been illustrated and methods used to determineK _I ,K _II , andσ _ox in five of the six states are given.     

Crack-tip dynamic isochromatics in the presence of small-scale yielding

A plasticity correction factor for the dynamic stress-intensity factor,K _I ^dyn , associated with a propagating crack tip in the presence of small-scale yielding, is derived from Kanninen's solution for a constant-velocity Yoffe crack with a Dugdale-strip yield zone. Distortions in the otherwise elastic isochromatics surrounding the constant-velocity crack tip are also studied by the use of this model. This plasticity correction factor is then used to evaluateK _I ^dyn from the dynamic isochromatics of a propagating crack in a 3.2-mm-thick polycarbonate wedge-loaded rectangular double-cantilever-beam specimen. The correctedK _I ^dyn is in good agreement with the corresponding values computed by a dynamic, elastic-plastic finite-element code executed in its generation mode.     

A photoelastic study of energy loss during a fracture event

Static and dynamic photoelastic experiments were conducted to evaluate the energy lost due to damping in a thick-walled-ring specimen during a run-arrest fracture event. Short starter cracks were machined into a series of ring specimens fabricated from Homalite 100 and the specimens were loaded by a specially designed mechanical deformeter to giveK _Q/K_Imranging from 1.76 to 2.15. The crack was initiated and high-speed photographs of the isochromatic-fringe loops at the tip of the running crack were recorded. The data were analyzed to obtain the instantaneous stress-intensity factorK(t), the normalized crack positiona/w, and the crack velocity \(\dot a\) . A comparison ofK, as a function of positiona/w, was made between static and dynamic crack growth. Average values ofK were determined from these curves and estimates of initial strain energy and energy lost in forming the fracture surface were made. An energy balance was used to evaluate the energy loss due to damping in all the experiments. The energy loss during the run-arrest event was approximately 50 percent of initial strain energy.     

Mixed-mode crack growth in plates under three-point bending

A combined theoretical and experimental study of the problem of crack growth in a plate subjected to unsymmetrical three-point bending was undertaken. The opening-modeK _I and sliding-modeK _II stress-intensity factors describing the local stress field around the crack tip were determined by a finite-element computer program. The crack growth was analyzed by the maximum circumferential stress and the minimum strain-energy density criteria. The critical loads for crack growth and the crack trajectories were determined both by theory and experiment. The experimental results corroborated the theoretical predictions.     

Analysis of dynamic mixed-mode isochromatics

The mixed-mode, elastodynamic state of stress in the neighborhood of a constant-velocity crack tip is used to generate numerically unsymmetric isochromatics. Unsymmetry associated with the third-order terms of a mixed-mode stress field, with and without the Mode II singular stress term, is also investigated. In extractingK _I from an unsymmetric isochromatic pattern, errors in the Mode I fracture parameters due to the assumed presence ofK _II in aK _I stress field were found to be significant when data are taken more than 4 mm from the crack tip. Paper was presented at V International Congress on Experimental Mechanics held in Montreal, Quebec, Canada on June 10–15, 1984.     

A bar impact tester for dynamic fracture testing of ceramics and ceramic composites

A bar impact test was developed to study the dynamic fracture responses of precracked ceramic bars, Al₂O₃ and 15/29-percent volume SiC_w/Al₂O₃. Crack-opening displacement was measured with a laser-interferometric displacement gage and was used to determine the crack velocity and the dynamic stress-intensity factorK _I ^dyn . The crack velocity andK _I ^dyn increased with increasing impact velocity while the dynamic-initiation fracture toughness,K _Id, did not vary consistently with increasing impact velocities.Paper was presented at the 1992 SEM Spring Conference on Experimental Mechanics held in Las Vegas on June 8–11.     

On the determination of the å-K relationship for birefringent polymers

Methods of utilizing dynamic photoelasticity with fracture-type specimens to simultaneously determine the stress-intensity factorK _Iand the crack-tip velocity are reviewed. Problems associated with data analysis to obtainK _Ifrom isochromatic-fringe loops are discussed. Errors resulting from the use of static near-field equations in the method of analysis are considered and a correction method is developed. Finally, the invariance ofK _Im(the minimumK required to maintain a finite crack velocity) is noted and evidence is provided to indicate thatK _Imcan be treated as a material propertly.Paper was presented at 1978 SESA Spring Meeting held in Wichita, KS on May 14–19.     

Further studies on dynamic crack branching

The newly derived dynamic-crack-branching criterion with its modifications is verified by the dynamicphotoelastic results of dynamic crack branchings in thinpolycarbonate, single-edged crack-tension specimens. Successful crack branching was observed in four specimens and unsuccessful branching in another. Crack branching consistently occurred when the necessary conditions ofK _I =K _{I b} =3.3 MPa \(\sqrt m\) and the sufficiency condition ofr _o =r _c =0.75 mm were satisfied simultaneously. In the unsuccessful branching test, the necessary condition was not satisfied sinceK _I was always less thanK _{I b} .     

Photoelastic determination of mixed-mode stress-intensity factorsK I,KII andK III

On the basis of existing photoelastic methods for the determination ofK _I andK _II, this paper presents an experimental method for determiningK _III with photoelastic data, and a photoelastic method for comprehensively determiningK _I,K _II andK _III under the complex stress condition. A frozen three-dimensional photoelastic model is first used to determineK _I andK _II from the slice perpendicular to the flaw edge. Then, from that slice, a sub-slice is taken to determine the factorK _III. This method is examined by comparison with two test models.     

Measurement of stress-intensity factor by means of a-c potential drop technique

A loading effect on a-c potential difference measured for two-dimensional stationary surface crack is examined under opening load without shear. An increment of potential difference caused by a load change is revealed to have a proportional relationship with an increment of the stress-intensity factor,K _I. Also, the constant of proportionality of the relationship is found to be independent of the crack length. Based on this relationship, a procedure is developed for measurement ofK _Iby means of the a-c potential drop technique.     

Dynamic stress-intensity-factor determination from isopachics

The governing equations for determination of dynamic stress-intensity factor at the tip of a running crack are developed from a dynamic analysis of dynamic isopachicfringe patterns. The equations are applied to investigate dynamic crack propagation in Homalite 100 by means of dynamic holographic interferometry. A simple method based on simultaneous measurement of the widths of two isopachics allows determination of Irwin's additional stress field, and a dynamic correction function for the stress-intensity factor is derived. It was found that dynamicK-values obtained from dynamic isopachic-fringe-pattern analysis are lower than their corresponding static values. This implies a modification of the crack velocity vs. stress-intensity-factor relationship towards lower values ofK for dynamic crack propagation.     

An investigation of propagating cracks by dynamic photoelasticity

A 16-spark gap, modified schardin-type camera was constructed for use in dynamic photoelastic analysis of fracturing plastic plates. Using this camera system, dynamic photoelastic patterns in fracturing Homalite-100 plates, 3/8 in. × 10 in. × 15 in. with an effective test area of 10 in. × 10 in., loaded under fixed grip condition were recorded. The loading conditions were adjusted such that crack acceleration, branching, constant velocity, deceleration and arrest were achieved. The Homalite-100 material was calibrated for static and dynamic properties of modulus of elasticity, Poisson's ratio, and stress-optical coefficient. For dynamic calibration, a Hopkinson bar setup was used to record the material response under constant-strain-rate loading conditions. The precise location of the dynamic isochromatic patterns in relation to the crack tip was determined by a scanning microdensitometer. This information was then used to determine dynamic stress-intensity factors which were compared with corresponding static stress-intensity factors determined by the numerical method of direct stiffness. Although the response of the dynamic stress-intensity factor to increasing crack length was similar to the static stress-intensity-factor response, the dynamic values were approximately 40 percent higher than the static values for constant-velocity cracks. for decelerating cracks, the peak values of dynamic stress-intensity factors were 40 percent higher than the corresponding static values.     

FEM analysis on mixed-mode fracture of CSM-GRP

A FEM analysis for studying mixed-mode fracture problem of chopped strand mat glass fibre reinforced polyester laminate is presented. The analysis is formulated on the basis of 8-node quadrilateral isoparametric element. The collapsed triangular quarter-point singular elements were used for calculating stress intensity factors K_Ι and K_Ⅱ.The crack propagation process was computed by implementing constraint release technique. Three different approaches to the solution of stress intensity factors K_Ι and K_Ⅱ were compared. The effect of constraint condition imposed upon the displacement of the three collapsed nodes of the crack tip elements on the K_Ι and K_Ⅱ results was evaluated. The mixed-mode critical stress intensity factors K_ΙC and K_ⅡC were estimated for CSM-GRP through the consideration of K_Ι and K_Ⅱ calculated and the measured failure load and critical crack length in the experiment.     

A novel method in determination of dynamic fracture toughness under mixed mode I/II impact loading

The objective of this paper is to propose a novel methodology for determining dynamic fracture toughness (DFT) of materials under mixed mode I/II impact loading. Previous experimental investigations on mixed mode fracture have been largely limited to qusi-static conditions, due to difficulties in the generation of mixed mode dynamic loading and the precise control of mode mixity at crack tip, in absence of sophisticated experimental techniques. In this study, a hybrid experimental–numerical approach is employed to measure mixed mode DFT of 40Cr high strength steel, with the aid of the split Hopkinson tension bar (SHTB) apparatus and finite element analysis (FEA). A fixture device and a series of tensile specimens with an inclined center crack are designed for the tests to generate the components of mode I and mode II dynamic stress intensity factors (DSIF). Through the change of the crack inclination angle β (=90°, 60°, 45°, and 30°), the K_II/K_I ratio is successfully controlled in the range from 0 to 1.14. A mixed mode I/II dynamic fracture plane, which can also exhibit the information of crack inclination angle and loading rate at the same time, is obtained based on the experimental results. A safety zone is determined in this plane according to the characteristic line. Through observation of the fracture surfaces, different fracture mechanisms are found for pure mode I and mixed mode fractures.     

Determination of the dynamic stress intensity factorsK I d andK II d,for a mixed-mode propagating crack

In this paper, the dynamic propagation problem of a mixed-mode crack was studied by means of the experimental method of caustics. The initial curve and caustic equations were derived under the mixed-mode dynamic condition. A multi-point measurement method for determining the dynamic stress intensity factors,K _I ^d , andK _II ^d , and the position of the crack tip was developed. Several other methods were adopted to check this method, and showed that it has a good precision. Finally, the dynamic propagating process of a mixed-mode crack in the three-point bending beam specimen was investigated with our method.     

Stress intensity factor and crack velocity relationship for polyester/TiO2 nanocomposites

The dynamic fracture behavior of polyester/TiO₂ nanocomposites has been characterized and compared with that of the matrix material. A relationship between the dynamic stress intensity factor,K _I and the crack tip velocity,å, has been established. Dynamic photoelasticity coupled with high-speed photography has been used to obtain crack tip velocities and dynamic stress fields around the propagating cracks. Birefringent coatings were used to conduct the photoelastic study due to the opaqueness of the nanocomposites. Single-edge notch tension and modified compact tension specimens were used to obtain a broad range of crack velocities. Fractographic analysis was conducted to understand the fracture process. The results showed that crack arrest toughness in nanocomposites was 60% greater than in the matrix material. Crack propagation velocities prior to branching in nanocomposites were found to be 50% greater than those in polyester.     

Resolved shear stress intensity coefficient and fatigue crack growth in large crystals

Fatigue crack growth is caused primarily by shear decohesion due to dislocation motion in the crack tip region. The resolved shear stress, which drives dislocation in a crystal, is strongly orientation dependent, and therefore, the cyclic plastic deformation of the shear decohesion process is highly anisotropic.The crack planes are often inclined to the loading axis both in the inplane orientation and in the thickness direction. This inclination induces all three modes of the crack tip stress field, K_I, K_II, and K_III.Fatigue crack growth in large-grain Al 7029 aluminum alloy was studied. The crack tip stress fields of the test specimens are calculated with the finite element method. The values of K_I, K_II, and K_III are evaluated. The orientation of the crystal at a crack tip was determined with the Laue X-ray method. The crystal orientation and the calculated crack tip stress fields are used to compute the resolved shear stress intensity of each of the twelve slip systems of the crystal at the crack tip. The resolved shear stress field of a slip system is linearly proportional to the resolved shear stress intensity coefficient, RSSIC.The values of RSSIC thus evaluated are used to analyze the orientations of the crack plane and to correlate with the shear fatigue crack growth rate.     

A Novel Experimental Approach for Calculating Stress Intensity Factors from Isochromatic Data

In the current paper a new method for calculating the stress intensity factor from isochromatic data is proposed. The method is based on the calculation of a map of the retardation using only the light- and dark-field images of a crack from a circular polariscope. The experimental retardation is compared with the theoretical one predicted by Westergaard’s model using between 700 and 800 data points in an array around the crack tip region. In this way, the necessity of unwrapping and calibrating the isochromatic fringe order distribution is avoided and a large potential source of error is eliminated. Subsequently, K_I, K_II and σ_ox are inferred by minimizing an error function. To show the potential and efficacy of the method, K values have been obtained from photoelastic images captured during fatigue tests conducted in a polycarbonate Center-Cracked-Tension (CCT) specimen. Results show an excellent level of agreement with those predicted from theory, highlighting the potential of the proposed methodology.     

Influence of indenter geometry on half-plane with edge crack subjected to fretting condition

An edge crack is analyzed to study fretting failure. A flat punch with rounded corners and a half-plane are regarded as an indenter and a substrate, respectively. Plane strain condition is considered. Contact shear traction in the case of partial slip is evaluated numerically. It is assumed that an initial crack is extended to the point of minimum strain energy density in the half-plane from the trailing edge of contact. Dislocation density function method is used to evaluate K_I and K_II. The variations of K_I and K_II during crack growth are examined in the case of indentation by a punch with different ratio of the flat region (l) to the punch width (L). Sih's minimum strain energy density theory [1] is also applied to predict the propagation direction of the initial crack. The direction evaluated is similar to that found in the experiment. Stress intensity factor ranges (ΔK_I and ΔK_II) are examined during cyclic shear on the contact. For the design of contacting bodies, a suggestible geometry of punch for alleviating cracking failure is studied.     

Axial crack propagation and arrest in a pressurized cylinder: An experimental-numerical analysis

The feasibility of using a previously developed crack-kinking criterion to predict crack arrest at a tear strap in a pressurized fuselage was studied with instrumented axial rupture tests of 21 models of an idealized fuselage. A rapidly propagating axial crack, which was initiated from a precrack, kinked immediately upon extension and propagated diagonally until it turned circumferentially and propagated along the tear straps. An elastodynamic finite element analysis of the rupturing model fuselage yielded the mixed-mode stress intensity factors,K _I andK _II , and the remote stress component, σ _OX . This numerical procedure was also used to predict the crack trajectories in full-scale fuselage rupture tests. All numerical results agreed well with their measured counterparts regardless of size.