Measurement Of Stress Intensity Factor Research Articles

Stress intensity factor evolution considering fracture process zone development of granite under monotonic and stepwise cyclic loading

Quasi-brittle materials like rocks may present mechanical non-linearity during cylic loading due to the formation of fracture process zone (FPZ), which poses a challenging task for accurate measurement of stress intensity factor (SIF). Understanding the crack development and SIF evolution under cyclic loading is beneficial for clarifying the mechanism of rock fatigue failure. Crack initiation and propagation are observed in semi-circular bending granite specimens subjected to monotonic and stepwise cyclic loading. Digital image correlation (DIC) and acoustic emission (AE) techniques are used to quantify the fracture behaviors through deformation fields and AE characteristic parameters. With the measured displacements around the notch, a novel J-integral method is coded and adopted to quantify the SIF at the crack tip which inherently takes the FPZ into account, and its validity is verified with synthetic images. Experimental results indicate that the development of the FPZ and SIF under cyclic loading is more complex than that under monotonic loading. The FPZ length, the SIF, and the crack opening displacement increase with the number of cycles in a specific loading level. For the loading level with a smaller upper load limit, the FPZ and SIF increase stably under repeated cycles, and AE events cluster in the first few cycles, exhibiting a significant Kaiser effect. As the upper load limit of the loading level increases, the FPZ and SIF increase linearly with the number of cycles, and the increase in the AE count rate and amplitude indicates the occurrence of abundant energetic microcracks under repeated loads. When the SIF at the crack tip approaches the fracture toughness of granite, the accelerated growth of the SIF in the last few cycles is accompanied by a rapid crack extension, resulting in a sharp rise in cumulative AE counts and energy.

An examination of techniques based on two strain gages for the determination of stress intensity factor [formula omitted

In this paper, Dally and Sanford [1] (DS) two strain gages technique (DS2) and a modified DS two strain gages technique (M_DS2) for accurate measurement of stress intensity factor (SIF) KI are studied. Accordingly, general finite element approaches are developed to estimate the extent of the radial locations of the strain gages in order to estimate the extent of the three- and four-term of the strain series proposed by DS. Also, to estimate the extent of validity of the proposed modified technique (M_DS2), which is a modification of the four-term strain series proposed by DS. A comparison between the results obtained by the technique of a single strain gage and the technique of two strain gages proposed by DS and the new technique is performed for four examples of configuration. Results of numerical examples show that the DS2 and M_DS2 can yield a highly accurate value of KI when the two strain gages are placed within the valid locations. Also, the results of numerical examples show that the above two strain gages techniques provide good solutions to ensure accurate measurement of KI, when the technique of a single strain gage unable to provide the desired precision and accuracy of KI in some configurations.

An optical method for measuring mixed-mode stress intensity factors for an arbitrarily oriented crack in cylindrical shells

This paper deals with the measurement of mixed-mode stress intensity factors for an arbitrarily oriented crack in cylindrical shells using an optical method based on a new theory of caustics. Completely analytical expressions are derived for caustic curves as well as for initial curves around the tip of an arbitrarily oriented crack in a cylindrical shell under mixed-mode conditions. The effects of mixed-mode condition, radius of curvature, shell thickness and crack angle on the caustic pattern are investigated, respectively. New procedures for the extraction of stress intensity factors KI and KII are presented using the characteristic dimensions of caustic patterns. A series of uniaxial tensile tests are performed on cylindrical shells containing an edge crack which is inclined to the axis of load by a different angle. The mixed-mode stress intensity factors obtained from the method of caustics developed here show a good agreement with previous theories and finite element results under K-dominant assumption.

Double Torsion testing of thin porous zirconia supports for energy applications: Toughness and slow crack growth assessment

Thin, porous zirconia-based ceramic components are of high interest in energy application devices where they are used as structural ceramics. Mechanical reliability of such devices is not only dependent on the fracture toughness of the ceramic components, but also on their sensitivity to slow crack growth (SCG). In this work, the fracture toughness and SCG behavior of porous (4.5–45.5%) and thin (∼ 0.25 mm) 3Y-TZP ceramics are investigated using the Double Torsion method. The analysis of the double torsion data, previously developed for dense materials, was here assessed and adapted. The compliance of the samples was observed to change linearly with crack length and the measured stress intensity factor was dependent on crack length, as for dense materials. This dependency decreased by increasing the sample porosity. For all materials, the ratio of the SCG threshold to fracture toughness was of 0.56 ± 0.06.

Higher sensitivity Digital Gradient Sensing configurations for quantitative visualization of stress gradients in transparent solids

Two modified full-field Digital Gradient Sensing (DGS) methods of higher measurement sensitivity relative to the prevailing ones are described for quantifying small angular deflections of light rays caused by stresses in transparent solids. These methods are devised by combining or altering previously proposed reflection-mode DGS (r-DGS) [1] and transmission-mode DGS (t-DGS) [2] methods. The concept involves increasing the optical path within the stressed medium by introducing an additional reflective surface behind the transparent solid, either as a separate reflector or as a rear surface reflective film deposition. The former approach is designated as t2-DGS method whose measurement sensitivity is twice that of t-DGS. The latter method results in an even higher sensitivity and is called the transmission-reflection DGS or tr-DGS method by making the back surface of a transparent planar solid reflective. The governing equations of tr-DGS are introduced first followed by a comparative demonstration of t2-DGS and tr-DGS methods by measuring the stress gradients in the crack-tip region during dynamic and static fracture experiments, respectively. Results show that tr-DGS is approx. 1.5 times more sensitive than t2-DGS, and at least three times more sensitive than t-DGS approach. Together as a family of DGS methods, these methods are used to extract the crack-tip stress intensity factors of PMMA beams under quasi-static loading conditions. The measured stress intensity factors are in good agreement with the predictions.

Measurement of stress intensity factor for modeⅠsurface crack by digital image correlation method

Measurement of stress intensity factor for modeⅠsurface crack by digital image correlation method

Real-Time and Quantitative Measurement of Crack-Tip Stress Intensity Factors Using Digital Holographic Interferometry

Detection of the crack in an object is a critical problem for the health monitoring of a transparent object. The real-time and quantitative measurement of the crack-tip stress intensity factor (SIF) remains an open issue. In this paper, an approach for real-time and quantitative measurement for the SIFs of a Mode I crack is presented based on digital holographic interferometry (DHI). A transmission digital holographic system is established to measure the phase difference of an object wave during loading. The expression to achieve the SIF from the phase difference is formulated. To enhance the accuracy of measurement, calibrated phase unwrapping based on least-squares and iteration and median filtering is applied to retrieve the actual phase from the noisy wrapped one. The SIFs of the Mode I crack in a transparent polymethyl methacrylate (PMMA) specimen are measured by this approach. The results are compared with the theoretical ones to demonstrate the feasibility of the proposed approach.

Measurement of opening displacement and stress intensity factor of two branches of bifurcated notch by Moiré interferometry

Static experiments on dynamic crack branching are carried out, in which Y-shaped notches in plate specimens are regarded as rapidly bifurcating cracks. Moiré interfrometry is applied to measure crack opening displacement, COD, of two branch notches as well as the mother notch of the Y-shaped notch. Stress intensity factor of the branch notches are calculated through the formula for COD of linear elastic fracture mechanics. From the measurement results, it is clarified that how far the singular stress field is developed around the branch crack tip.

Accurate Measurement of Mixed Mode (I/II) Stress Intensity Factors Using Strain Gages

Abstract Determination of accurate mixed mode stress intensity factors forms the basis for the understanding and analysis of mixed mode fracture. In this context, experimental methods for the measurement of stress intensity factors (SIFs) play a vital role. However, very few strain gage based techniques are available for measurement of mixed mode SIFs KI and KII in isotropic materials. In addition, no useful recommendations on appropriate radial locations of strain gages ensuring accurate SIFs are available in literature. Recently, authors have theoretically proposed a mixed mode strain gage technique and attempted to address the long standing problem of assessment of appropriate strain gage radial locations for the accurate measurement of the SIFs. They have shown that there exist certain gage radial locations called as optimal locations for the accurate measurement of SIFs, which can be easily assessed with their proposed methodology for any mixed mode (I/II) configurations. In the present investigation, experiments were conducted to study the efficacy of the authors' proposed mixed mode strain gage technique and existence and usefulness of the optimal strain gage locations in accurate measurement of SIFs KI and KII. The present experiments were also aimed to show the consequences of placing the gages at invalid or non-optimal gage locations. The experimental results clearly show that highly accurate mixed mode SIFs can be measured using the proposed mixed mode strain gage technique if the gages are pasted at the optimal locations. On the other hand, the results also exposed that highly erroneous and unacceptable measurement of SIFs can result if the gages are located at non-optimal locations. Furthermore, the present results clearly demonstrated the need of knowing the optimal strain gage locations a priori, which can be assessed using the methodology proposed recently by the authors.

Dynamic mixed-mode fracture behaviors of PMMA and polycarbonate

Mixed-mode dynamic crack initiation and growth in polymethymethacrylate (PMMA) and polycarbonate (PC) are studied experimentally. A simple specimen geometry in conjunction with a dynamic loading configuration to generate different mode-mixities at crack initiation is demonstrated. A Hopkinson pressure bar is used to rapidly load free-standing edge cracked samples in a reverse impact configuration. By eccentrically loading the specimen relative to the crack line, various mode-mixities at crack initiation are achieved by increasing the initial crack length while keeping all other experimental parameters the same. A relatively new full-field optical technique, Digital Gradient Sensing (DGS), along with high-speed photography is used to perform full-field measurements. DGS measures instantaneous angular deflections of light rays representing two orthogonal stress gradients under plane stress conditions. The mode-I and -II stress intensity factor histories are evaluated via over-deterministic least-squares analysis of optically measured data. By quantifying the critical stress intensity factors evaluated at crack initiation, dynamic fracture envelopes are developed for both the polymers. The results are studied comparatively and relative to the brittle fracture criteria. From measured stress intensity factors and crack speeds in the post-initiation regime, energy release rate vs. velocity plots for different mixed-mode configurations are produced for both the polymers.

Digital Image Correlation Using Specific Shape Function for Stress Intensity Factor Measurement

The stress intensity factor (SIF) is a critical parameter associated with the fracture behaviour of materials. In this paper, we select the displacement function around a crack tip as the shape function of the digital image correlation (DIC), which makes it possible to directly calculate the SIF by the correlation scheme. Moreover, we use a non-rectangular subset, which can reduce the influence of plastic deformation and crack width on the DIC measurement accuracy. We measured the SIF of a mode I crack in a super-hard aluminium alloy specimen to verify the performance of the proposed method. Our experimental results show that a DIC with a specific shape function can be used to accurately and efficiently calculate the SIF. Furthermore, we also present a practical application of our proposed method for determining the SIF, crack propagation angle and crack tip displacement.

A J-integral approach using digital image correlation for evaluating stress intensity factors in fatigue cracks with closure effects

Digital image correlation (DIC) techniques are used to obtain the stress intensity factor (SIF) via experimental J-integral evaluations in an AISI 4340 steel disk-shaped compact-tension (DC(T)) specimen subjected to mode I loading conditions. The combined analytical and experimental methodology is based on the computation of the J-integral over an arbitrary but elastic contour path enclosing the crack tip. The DIC displacement field around the crack is used to directly determine the displacement gradients, the stress components, and the total strain energy for points along the selected path employing stress-strain linear elastic relations. The proposed analytical-experimental hybrid approach is then applied to investigate the influence of crack closure on SIF measurements under constant amplitude loading conditions, after and before the application of overloads. The effects of the closure-induced nonlinearities observed in the experimental results are analyzed and discussed.

モードI表面き裂を対象としたデジタル画像相関法による応力拡大係数と有効応力拡大係数範囲の計測

モードI表面き裂を対象としたデジタル画像相関法による応力拡大係数と有効応力拡大係数範囲の計測

Experimental and computational investigation of the effect of phase transformation on fracture parameters of an SMA

A comprehensive, multi-method experimental characterization of fracture is conducted on shape memory alloy NiTi that exhibits superelasticity due to austenite-to-martensite stress induced phase transformation. This characterization includes (i) load-based measurement of critical stress intensity factor (Kmax) using ASTM standard E399, (ii) measurement of crack tip opening displacement (CTOD) per ASTM standard E1290, (iii) the digital image correlation (DIC) characterization of the transformation zone as well as the displacement-field based measurement of Kmax from the DIC data. Samples have also been tested at T = 100 °C to suppress the martensitic transformation to investigate transformation toughening. The experimental investigation is complemented with finite element (FE) analysis that uses Auricchio–Taylor–Lubliner constitutive model. A direct observation with DIC revealed a small scale transformation (K-dominance). Kmax of the transforming material is higher than that of the transformation-suppressed material tested at 100 °C, suggesting transformation toughening. At 100 °C, the material becomes quite brittle with a very small crack-tip plastic zone when the transformation mechanism is blocked. By measures of critical CTOD, the gap widens even more between the superelastic and transformation-suppressed cases, particularly because of the side effect that, in this very interesting material, material modulus increases with temperature. Evaluating the transformation zone from the DIC strains with reference to the uniaxial stress–strain curve, an equivalent strain form is proposed in conjunction with the plane stress FE prediction.

混合モード下における近接分布ノッチの応力拡大係数の測定について

混合モード下における近接分布ノッチの応力拡大係数の測定について

Stress Intensity Factor Measurement of Inclined Crack in Tensile Plates by Use of Photoelasticity

This paper presents the measurement of stress intensity factors of inclined cracks by use of photoelasticity. The distributions of isochromatics near a crack tip of the specimen loaded by uniaxially tensile load are used for analysis. Accuracy and reliability is enhanced by twice multiplying and sharpening the measured isochromatics using digital image processing. Photoelastic results are compared with those obtained by finite element method. Good agreement between them shows that the photoelastic analysis is reliable.

현무암섬유 섬유 배향에 따른 현무암섬유 강화 복합재료의 기계적 계면특성 영향

본 연구에서는 현무암섬유의 계면을 황산과 과산화수소로 처리하고 섬유 배향각을 <TEX>$0^{\circ}$</TEX>, <TEX>$0^{\circ}/90^{\circ}$</TEX>, <TEX>$0^{\circ}/45^{\circ}/-45^{\circ}$</TEX>로 달리하여 현무암섬유 에폭시 강화 복합재료의 기계적 특성에 미치는 영향에 대해서 살펴보았다. 기계적 특성은 층간 전단강도(ILSS)와 파괴인성 요소 중 임계응력세기인자(<TEX>$K_{IC}$</TEX>) 측정을 통하여 고찰하였으며, 섬유의 표면미세구조 변화와 복합재료의 파단면은 주사전자현미경(SEM)으로 관찰하였다. 또한 섬유표면에 계면처리의 여부를 확인하기 위하여 적외선 분광법(FTIR)과 X-선 광전자 분광법(XPS)을 분석하였다. 실험결과 계면처리한 섬유 표면의 -OH 기(hydroxyl)가 증가됨을 확인하였다. 계면처리한 후의 기계적 특성이 계면처리 전의 기계적 특성보다 약 ~100% 증가하였다. 이러한 결과는 표면처리에 의해 섬유와 에폭시 수지 매트릭스 사이의 계면결합력을 증가시킨 것으로 판단된다. In this work, the effect of fiber array direction including <TEX>$0^{\circ}$</TEX>, <TEX>$0^{\circ}/90^{\circ}$</TEX>, <TEX>$0^{\circ}/45^{\circ}/-45^{\circ}$</TEX> was investigated for mechanical properties of basalt fiber-reinforced composites. Mechanical properties of the composites were studied using interlaminar shear strength (ILSS) and critical stress intensity factor (<TEX>$K_{IC}$</TEX>) measurements. The cross-section morphologies of basalt fiber-reinforced epoxy composites were observed by scanning electron microscope (SEM). Also, the surface properties of basalt fibers were determined by Fourier transform infrared spectroscopy (FTIR) and X-ray photoelectron spectroscopy (XPS). From the results, it was observed that acid treated basalt fiber-reinforced composites showed significantly higher mechanical interfacial properties than those of untreated basalt fiber-reinforced composites. These results indicated that the hydroxyl functional groups of basalt fibers lead to the improvement of the mechanical interfacial properties of basalt fibers/epoxy composites in the all array direction.

104 モードI表面き裂を対象としたデジタル画像相関法による有効応力拡大係数の計測(材料力学I)

104 モードI表面き裂を対象としたデジタル画像相関法による有効応力拡大係数の計測(材料力学I)

122 光干渉法による高速分岐き裂の動的応力拡大係数測定

122 光干渉法による高速分岐き裂の動的応力拡大係数測定

Direct Measurement of Opening Mode Stress Intensity Factors Using Flexoelectric Strain Gradient Sensors

This paper presents a new method for direct measurement of Mode-I stress intensify factor of cracks using Ba0.64Sr0.36TiO3 flexoelectric strain gradient sensors. Firstly, strain gradient field around the opening mode crack tip was analyzed, followed by the derivation of induced flexoelectric polarization in the strain gradient sensors attached in the vicinity of a crack tip. It was found that the constant stress term makes no contribution to the strain gradient, thus the flexoelectric output directly reflects the singular effect. This unique property eliminates the special requirement for sensor placement coordinates and improves the accuracy of the stress intensify factor predication. A specimen with Mode-I crack was then prepared with two strain gradient sensors (4.7 mm × 0.9 mm × 0.3 mm) attached close to the crack tip to verify the analytical model for measurements of stress intensity factor. The experimental results matched well with the empirical estimation confirming that flexoelectric strain gradient sensing can be a convenient and accurate avenue for measuring the stress intensify factor.