Measurement Of Stress Intensity Factor Research Articles

A PVDF Sensor for the In-situ Measurement of Stress Intensity Factors During Fatigue Crack Growth

Several analytical and numerical studies of inverse analysis are performed to verify the feasibility and accuracy of the proposed K-sensor. At first, the application to cracks in sheets under in-plane stresses is investigated and compared with the analytical solution for the GRIFFITH's crack under mixed mode. It was found that the convergence radius, where the electrodes have to be placed, must be smaller than half of the crack length, which is sufficient for real cracks of several millimeters. The obtained accuracy of crack tip location and (KI, KII)-factors is better than 1%. Second, the technique is applied to cracks in thin-walled plates of KIRCHHOFF type under bending and torsion moments. In this case, the plate intensity factors (k1, k2) are of interest. Again, the inverse identification procedure is studied by synthetic analytical and numerical solutions of simple crack configurations. Due to the assumptions of the KIRCHHOFF plate model, the sensors have to be placed outside a radius of 3 times plate thickness h. The obtained accuracy in position and intensity factors is quite sufficient as well. The practical realization of the K-factor sensor requires good electric signal measurement and amplification. Its experimental testing on components is ongoing work.

Anisotropic Stress Intensity Factor Ranges Measurements with DIC

The effect of anisotropy on fatigue crack growth was studied using the stress intensity factor range in single crystal specimens. The material tested was the nickel based superalloy Haynes 230. Two different crystal orientations were cyclically loaded. Once a crack was observed, the entire loading and unloading process was optically recorded and the evolution of the displacements around the crack tip was obtained in terms of digital image correlation. Stress intensity factor ranges (ΔKI and ΔKII), together with T-stress, were extracted using a least-squares regression algorithm, based on the theoretical crack tip displacement in an anisotropc body. DIC displacements included crack closure effects, allowing the direct measurement of the effective stress intensity factor ranges. Crack propagation in the [001] crystal was only driven by ΔKI, since the displacement field around the crack tip was symmetric and no L1KII was measured On the other hand, the displacement field around crack tip in [111] crystal showed an asymmetric displacement profile, highlighting the presence of Mode II sliding. As expected, ΔKII measured by regression was found to be higher than ΔKI: this result was due to the crack angle, which was 55°.

MFC센서를 이용한 피로수명예측에 관한 연구

Abstract The large-scale structures have the possibility that there are defects such as cracks due to stress concentrationcaused by geometric discontinuities in the structure. In this respect, the assessment of fatigue life and the development of structural health monitoring(SHM) are very important. Fatigue design of structure is typically accomplished either using a set of stress cycle (S-N) data obtained from fatigue tests or using the fracture mechanics approach. The stress intensity factor(SIF) is required for the estimation of fatigue crack propagation life from the linear elastic fracture mechanics (LEFM) perspective. In this study, Macro Fiber Composie(MFC) sensor for the measurement of SIF of two dimensional cracks is used. The SIF based on the piezoelectric constitutive law and fracture mechanics are calculated. The measured values of the SIF are later used for the prediction of the crack propagation life. In this study, the measured value of the SIF and the fatigue life are compared with the theoretical results.Key Words : MFC sensor, Stress intensity factor(SIF), Fatigue crack propagation life

Morphology and fracture toughness of nanostructured epoxy thermosets containing macromolecular miktobrushes composed of poly(ε-caprolactone) and polydimethylsiloxane side chains

In this work, we investigated the nanostructures and mechanical properties of epoxy thermosets containing a macromolecular miktobrush composed of poly(e-caprolactone) (PCL) and polydimethylsiloxane (PDMS) side chains. The novel macromolecular miktobrush was synthesized via the combination of reversible addition–fragmentation chain transfer and ring-opening polymerizations. In the brush-like copolymer the molar ratio of PCL to PDMS was controlled to be 1:1 and the length of PCL chains was controlled to be close to that of PDMS chains (i.e., L PDMS = 1000). The densely grafted miktobrush copolymer was incorporated into epoxy and the nanostructured thermosets were obtained as evidenced by means of transmission electron microscopy and dynamic mechanical thermal analysis. The results of small-angle X-ray scattering showed that the formation of nanostructures in the thermosets followed a self-assembly mechanism. The measurement of critical stress intensity factor (K 1C) showed that the nanostructured thermosets displayed the improved fracture toughness owing to the formation of nanostructures.

무전해 니켈도금된 다중벽 탄소나노튜브의 첨가가 알루미나강화 에폭시 복합재료의 열전도도 및 파괴인성에 미치는 영향

본 연구에서는 무전해 니켈도금에 따른 탄소나노튜브의 표면특성변화가 알루미나강화 에폭시 복합재료의 열전도도 및 파괴인성에 미치는 영향에 대하여 살펴보았다. 무전해 니켈도금된 탄소나노튜브의 표면특성은 주사전자현미경(SEM), X-선 광전자분광기(XPS), X-선 회절분석(XRD)을 통하여 알아보았다. 열전도도는 열전도율 측정 시스템으로 측정하였고, 파괴인성은 만능시험기(UTM)를 이용한 임계응력세기인자(<TEX>$K_{IC}$</TEX>)를 측정하여 분석하였다. 실험결과, 무전해 니켈도금은 탄소나노튜브의 표면특성의 변화를 가져오며, 니켈도금된 MWCNTs(Ni-MWCNTs)가 들어있는 경우 미처리 MWCNTs와 비교하여 우수한 열전도도 및 파괴인성을 보였다. 이는 Ni-MWCNTs와 에폭시수지와의 분자간 상호작용의 향상 때문이라 판단된다. In this work, the effect of electroless Ni-plating of multi-walled carbon nanotubes (MWCNTs) on thermal conductivity and fracture toughness properties of MWCNTs/<TEX>$Al_2O_3$</TEX>/epoxy composites was investigated. The surface properties of the Ni-plated MWCNTs were determined by scanning electron microscopy (SEM), X-ray photoelectron spectrometry (XPS), and X-ray diffraction (XRD) analyses. Thermal conductivity was tested using a thermal conductivity measuring system. The fracture toughness of the composites was carried out through the critical stress intensity factor (<TEX>$K_{IC}$</TEX>) measurement. As a result, the electroless Ni-plated MWCNTs led to a significant change of surface characteristics of the MWCNTs. Thermal conductivity and fracture toughness of the MWCNTs/<TEX>$Al_2O_3$</TEX>/epoxy composites were greater than those of non-treated ones. These results were probably due to the improvement of intermolecular interaction between the Ni-MWCNTs and the matrix resins.

Experimental investigation of spur gear tooth mesh stiffness in the presence of crack using photoelasticity technique

Gear mesh stiffness plays a very important role in gear dynamics and it varies in the presence of gear fault such as crack. The measurement of stress intensity factor can lead to the determination of gear tooth mesh stiffness variation in the presence of crack in a spur gear system. In this paper, the technique of conventional photoelasticity has been revisited to explore the possibility of using it as a supplementary technique to experimentally measure the variation of gear mesh stiffness. An attempt has been made to calculate the variation of mesh stiffness for a pinion having a cracked tooth and a gear tooth with no crack of a spur gear pair. An analytical methodology based on elastic strain energy method in conjunction with total potential energy model has been adopted and implemented within the mesh stiffness calculations. To visualize the state of stress in a structure using finite element and other currently available methods, photoelasticity is considered to be one of the oldest and most developed experimental technique. An experimental methodology based on conventional photo-elasticity technique for computing stress intensity factor (SIF) for cracked spur gear tooth is presented for different single tooth contact position and crack length. The relation between contact position, crack length, crack configuration, SIF and the variation of total effective mesh stiffness have been quantified. Finally, a comparison has been made and the results obtained from finite element method (FEM) based on linear elastic fracture mechanics (LEFM), analytical method and proposed experimental method has been outlined.

알루미나 나노섬유와 분말이 첨가된 에폭시 복합재료의 열전도도 특성 및 파괴인성에 대한 연구

본 연구에서는 알루미나 나노섬유의 함량을 20에서 100 phr까지 달리하여 알루미나 나노섬유와 분말이 첨가된 에폭시 복합재료의 열전도도 및 파괴인성에 미치는 영향에 대해서 살펴보았다. 열전도도는 열전도도분석기로 측정하였고, 파괴인성은 임계응력세기인자(<TEX>$K_{IC}$</TEX>) 측정을 통하여 고찰하였다. 모폴로지는 주사전자현미경(SEM)으로 관찰하였다. 실험결과, 알루미나 나노섬유의 함량이 증가함에 따라 열전도도가 향상됨을 확인할 수 있었으며, 알루미나 나노섬유의 함량이 열전도도를 결정하는 중요한 요소임을 알 수 있었다. <TEX>$K_{IC}$</TEX> 값도 알루미나 나노섬유의 함량이 증가할수록 큰 값을 가지는 것을 확인할 수 있었으나 40 phr 이상에서는 오히려 감소하였다. 이는 과량의 알루미나 나노섬유가 에폭시 내에서 서로 뭉침으로 인하여 <TEX>$K_{IC}$</TEX> 값을 감소시킨 것으로 판단된다. In this work, the effect of alumina nanofibers on thermal conductivity and fracture toughness of alumina nanofibers and powder filled epoxy (EP) composites were investigated with varying alumina nanofiber content from 20 to 100 phr. Thermal conductivity was tested using a laser flash analysis (LFA). The fracture toughness of the composites were studied through the critical stress intensity factor (<TEX>$K_{IC}$</TEX>) measurement. The mophologies were observed by scanning electron microscopy (SEM). From the results, it was found that the thermal conductivity was enhanced with increasing alumina nanofiber content, which played a key factor to determine the thermal conductivity. The <TEX>$K_{IC}$</TEX> value was increased with increasing alumina nanofiber content, whereas the value decreased above 40 phr alumina nanofiber content. This was probably considered that the alumina nanofiber entangled each other in EP due to an excess of alumina nanofibers.

OS1804 コースディック法を用いた混合モード応力拡大係数測定に及ぼす3次元応力場の影響

Three-dimensional (3-d) stress field exists in the very vicinity of a crack tip within the singular stress field of plane stress. The paper examines the effect of the 3-d field to the measurement of stress intensity factors by the caustic method where the crack is under the mixed mode loading of mode I and II. The experimental studies show that the 3-d field extends as far as half the thickness of plate specimens under the mixed mode loading condition. This result is the same as that of mode I loading. The values of KI in the 3-d field are smaller than the true K_I value, and those of K_<II> in the 3-d field are larger than the true value of K_<II>.

EVALUATING STRESS INTENSITY FACTOR OF POLYCARBONATE USING DIGITAL IMAGE CORRELATION

The application of the digital image correlation (DIC) method to determine the stress intensity factor (SIF) for cracks in Polycarbonate is proposed in this paper. Standard compact tension specimen was tested under tensile loading and the full-field displacement fields of the test sample were recorded using DIC. According to linear elastic fracture mechanics, the SIF associated with unavoidable rigid-body displacement translation and rotation were calculated simultaneously from the experimental data by fitting the theoretical displacement field using the method of least-squares. Selection of displacement and convergence values is discussed. The effectiveness and accuracy of the proposed technique is verified by comparison with theoretical results, which reveals that the DIC is a practical and effective tool for full-field deformation and SIF measurement.

Monitoring fatigue cracks and stress intensity factors based on local strains

AbstractA method for crack detection and stress intensity factor measurement in plate structures is presented by using strain gauges and applying the Body Force Method (BFM). The BFM is based on elastic solutions for concentrated loads and the principle of linear superposition allowing e.g. the calculation of the strain field in a cracked body. The inverse problem is solved applying the PSO (particle swarm optimization) and the unknown parameters are crack position, length and inclination as well as loading quantities. Experiments are carried out under cyclic loading using pre‐cracked plates made of aluminum alloy. (© 2012 Wiley‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Monitoring Fatigue Cracks and Stress Intensity Factors Based on the Distributed Dislocation Technique

We present a method for crack detection and stress intensity factor measurement in plate structures by using strain gauges and applying the dislocation method. The presented approach is based on the strain measured at different locations on the surface of the structure. This allows both the identification of crack position parameters, such as length, location and angles with respect to a reference coordinate system and the calculation of stress intensity factors (SIF). The method solving the direct problem is based on the idea of representing the crack by a line of point dislocations. The latter are formed by applying a constant displacement between adjacent points located at either side of the crack. Thus, the approach is based on the weighted superposition of elastic Greens functions representing the strain field due to the presence of a crack, where the weights are being identified by inverse problem solution. Since the strain fields are controlled by both external loads and the crack growth the unknown parameters are crack length, position and inclination as well as loading quantities. The particle swarm algorithm (PSO) came out to be most suitable for parameter identification in a high dimensional space.

다중벽 탄소나노튜브강화 폴리프로필렌 나노복합재료의 전자파 차폐효과 및 기계적 특성

본 연구에서는 다중벽 탄소나노튜브(MWCNT)의 함량을 1에서 10 wt%까지 달리하여 MWCNT 강화 폴리프로필렌(PP) 나노복합재료의 전자파 차폐효과 및 기계적 특성에 미치는 영향에 대해서 살펴보았다. 전기전도도는 4단자법으로 측정하였고, 전자파 차폐효과는 흡수와 반사방법으로 분석하였다. 기계적 특성은 임계응력세기인자(<TEX>$K_{IC}$</TEX>) 측정을 통하여 고찰하였으며, 모폴로지는 주사전자현미경(SEM)으로 관찰하였다. 실험결과, MWCNT의 함량이 증가함에 따라 차폐효과가 향상됨을 확인할 수 있었으며, MWCNT의 함량이 전자파 차폐효과를 결정하는 중요한 요소임을 알 수 있었다. <TEX>$K_{IC}$</TEX>값도 MWCNT의 함량이 증가할수록 큰 값을 가지는 것을 확인할 수 있었으나 5 wt% 이상에서는 오히려 감소하였다. 이는 과량의 MWCNT가 PP 내에서 서로 뭉침으로 인하여 <TEX>$K_{IC}$</TEX>값을 감소시킨 것으로 판단된다. In this work, the effect of multi-walled carbon nanotube (MWCNT) on electromagnetic interference shielding effectiveness (EMI SE) and mechanical properties of MWCNT-reinforced polypropylene (PP) nanocomposites were investigated with varying MWCNT content from 1 to 10 wt%. Electric resistance was tested using a 4-point-probe electric resistivity tester. The EMI SE of the nanocomposites was evaluated by means of the reflection and adsorption methods. The mechanical properties of the nanocomposites were studied through the critical stress intensity factor (<TEX>$K_{IC}$</TEX>) measurement. The morphologies were observed by scanning electron microscopy (SEM). From the results, it was found that the EMI SE was enhanced with increasing MWCNT content, which played a key factor to determine the EMI SE. The <TEX>$K_{IC}$</TEX> value was increased with increasing MWCNT content, whereas the value decreased above 5 wt% MWCNT content. This was probably considered that the MWCNT entangled with each other in PP due to an excess of MWCNT.

Full field measurements of anisotropic stress intensity factor ranges in fatigue

The effects of anisotropy during mixed mode fatigue crack growth were studied in single crystal 316L stainless steel. An anisotropic least-squares regression algorithm using displacements from digital image correlation was developed to find the effective stress intensity factors, KI and KII, and the T-stress. Crack tip plastic zones were determined using an anisotropic yield criterion. Strains in the plastic zone obtained from digital image correlation showed a dependence on the crystallography and load ratio. Crack tip slip irreversibility was measured and showed an increasing trend with increasing crack length; this information is critical for describing crack growth behavior.

Dynamic fracture of graphite/epoxy composites stiffened by buffer strips: An experimental study

Fracture responses of unidirectional graphite/epoxy composite coupons enhanced by buffer strips are investigated under impact loading conditions using digital image correlation technique and high-speed photography. Composite coupons made of phenylethynyl terminated imide oligomer (PETI-5) as matrix and IM7 graphite fiber as reinforcement are studied. Buffer strips are made of the same material but with a different stacking sequence to attain quasi-isotropy. Edge-notched coupons are subjected to impact loading along the axis of symmetry. The effectiveness of methods used for attaching the buffer strip, namely, co-curing at elevated temperatures and adhesive bonding at room temperature, are also examined. The optically measured stress intensity factor histories reveal that both methods provide nearly identical fracture responses. However, the crack initiates much later in coupons stiffened using adhesive bonding method than its co-cured counterpart and thus shows higher stress intensity factor at initiation. The residual stresses are shown to be responsible for the difference in the fracture responses.

Measurement of mixed-mode stress intensity factors using digital image correlation method

Applications of the digital image correlation method (DIC) for the determination of the mixed-mode stress intensity factors (SIF) is investigated in this paper. Experiments were performed on an edge fatigue cracked aluminum specimen using a special loading device, which is an appropriate apparatus for experimental mixed-mode fracture analysis. The full-field displacements around the crack-tip region of the test sample were calculated using DIC. And then the SIF associated with unavoidable rigid-body displacement motion were calculated simultaneously from the experimental data. The effect of the rigid body motion on the measured displacements was then eliminated using the computed rigid body translation and rotation. A coarse-fine searching method was developed to determine the crack-tip location. For validation, the SIF thus determined is compared with theoretical results, confirming the effectiveness and accuracy of the proposed technique. Therefore it reveals that the DIC is a practical and effective tool for full-field deformation and SIF measurement.

1405 引裂き試験による竹の限界応力拡大係数の測定(OS15-1 諸観点からの物質・材料の特性評価I,OS15 諸観点からの物質・材料の特性評価)

1405 引裂き試験による竹の限界応力拡大係数の測定(OS15-1 諸観点からの物質・材料の特性評価I,OS15 諸観点からの物質・材料の特性評価)

Extent of Three Parameter Zone and Optimum Strain Gage Location for Eccentric Cracked Configurations

The accuracy of measurement of opening mode stress intensity factor using strain gage techniques mainly depends on location of the strain gages. The present work proposes a finite element based simple procedure for accurate determination of three parameter zone and optimum strain gage location for various eccentric cracked configurations. In this paper, the effect of specimen size and crack length to width of the eccentric cracked plate on optimum location of strain gage is also studied. The results of the present investigation show that specimen size and ratio of crack length to width of the plate strongly influence the optimum location of strain gage.

Nanostructured thermosets from epoxy and poly(2,2,2-trifluoroethyl acrylate)- block-poly(glycidyl methacrylate) diblock copolymer: Demixing of reactive blocks and thermomechanical properties

Poly(2,2,2-trifluoroethyl acrylate)- block-poly(glycidyl methacrylate) (PTFEA- b-PGMA) diblock copolymer was synthesized via sequential reversible addition-fragmentation chain transfer (RAFT) polymerization. The reactive diblock copolymer was incorporated into epoxy to obtain the nanostructured thermosets. The morphology of the thermosets was investigated by means of atomic force microscopy (AFM) and small-angle X-ray scattering (SAXS). It is identified that the demixing of the reactive subchain ( viz. PGMA) out of epoxy matrix occurred in the process of curing reaction, which exerted a profound impact on the glass transition temperatures of the nanostructured thermosets. The static contact angle measurements showed that the nanostructured thermosets displayed a significant enhancement in surface hydrophobicity as well as a reduction in surface free energy. The improvement in surface properties was attributed to the enrichment of the fluorine-containing block (i.e., PTFEA) of amphiphilic diblock copolymer on the surface of the thermosets, which was further evidenced by surface atomic force microscopy (AFM). The measurement of critical stress intensity factor ( K 1C) showed that the fracture toughness of the materials was significantly enhanced by the inclusion of a small amount of PTFEA- b-PGMA diblock copolymer.

Identification of damage and cracking behaviours based on energy dissipation mode analysis in a quasi-brittle material using digital image correlation

Characterizing the crack stability to predict the behaviour of ceramics designed for industrial use is a challenging issue. It requires accurate crack tip detection during the controlled crack propagation of notched bending tests. Different indirect methods are available, like for instance the compliance technique. Recently, techniques based on digital image correlation (DIC) have emerged: finite-element DIC (FE-DIC) with a finite element decomposition of the displacement field, integrated-DIC (I-DIC) based on Williams’ series decomposition of the displacement field and regularized-DIC (R-DIC) for mechanical constraints. These full-field techniques enable the quantification of the crack length and the stress intensity factor K I . In this paper, these four methods are compared in terms of measurements of crack lengths and stress intensity factors during a notched bending test. The tested material is a damageable quasi-brittle ceramic at room temperature. The non linearity of the stress-strain law of this microcraked ceramic results in a complex behaviour that is not captured by the compliance method during the bending test. Therefore the linear elastic compliance method leads to a different estimation of crack lengths and stress intensity factors compared to DIC methods. On the other hand, the R-DIC approach handles the non linear material constitutive behaviour. It allows a deeper analysis of the mechanical fields, the energy dissipation and the damage mechanisms during the crack propagation.

The Stress Intensity Factor of Opening Mode Determined by Digital Image Correlation

Applications of the digital image correlation method (DIC) for the determination of the opening mode stress intensity factor (SIF) is investigated using an edge cracked aluminum plate in this paper. Standard compact tension test specimen was tested under tensile loading and the full-field displacement fields of the test sample were recorded using DIC. The SIF associated with unavoidable rigid-body displacement translation were calculated simultaneously from the experimental data by fitting the theoretical displacement field using the method of least-squares. Selection of displacement and convergence values is discussed. For validation, the SIF thus determined is compared with theoretical results, confirming the effectiveness and accuracy of the proposed technique. Therefore it reveals that the DIC is a practical and effective tool for full-field deformation and SIF measurement.