Multiple cracking of a coating layer and its influence on fibre strength

A calculation method to describe the influence of the non-uniform crack-spacing in a strongly adhering coating layer, which shows multiple cracking, on the energy release rate of a coated fibre is presented and applied to some examples. Four main results were found. The energy release rate of the fibre at the crack in the region of narrow crack-spacing was low. For any crack-spacing, the energy release rate was high when the Young's modulus of the fibre was low and that of the coating layer was high. From the calculation of energy release rates of the fibre at all cracks, the strength-determining crack could be identified, and from this the fibre strength after multiple cracking of the coating layer could be estimated. Finally, the strength of the fibre for non-uniform crack spacing was lower than that for a uniform one.     

Multiple cracking of a coating layer and its influence on fibre strength

Multiple cracking of a coating layer and its influence on the tensile strength of the coated fibre in the case of strong interfacial bonding were simulated by means of a Monte Carlo method. Within the range where the coating layer was weak, it was found that the weaker the coating layer, the larger became the number of cracks and consequently the smaller became the crack spacing, resulting in higher strength of the fibre. When the strength of the layer was high, however, the crack spacing became large, resulting in a low strength of the fibre comparable to the strength for the case of single cracking. The strength value of the fibre calculated for average crack spacing gave an upper bound, and that calculated for single cracking a lower bound, for the actual fibre strength.     

Statistical Model of Coating Fragmentation Under Equibiaxial Load

A statistical model of coating cracking under equibiaxial tension is proposed based on a Weibull strength distribution for the coating. Crack length and spacing distributions are derived assuming that cracks initiate in random locations and propagate straight till stopping upon encountering a geometiical obstacle (another crack). The theoretical distributions are verified by comparing with simulated cracking patterns obtained by the Monte-Carlo method. An analysis of crack patterns of SiO₂ coatings on a PET film under biaxial tension is performed. Qualitative agreement with the theoretical crack spacing distribution is observed.     

Crack spacing statistics and spalling area fractions for indented silica-coated bismaleimide (BMI)

Indentation loading of thin, continuous silica coatings adhered to Bismaleimide (BMI) polymeric substrates induces a concentric array of cracks in the silica coating. For Vickers indentation, the array consists of diamond-shaped concentric cracks, while Hertzian indentation gives circular concentric cracks. This paper characterizes the indentation-induced crack damage in the coating in terms of: (1) f _s, the area fraction of the coating (within the indentation-cracked region) that spalls off the substrate due to the indentation and (2) the spacing between the cracks in the crack array. For a given indentation crack field, the crack spacing was uniform as a function of radial distance outward from the center of the indentation. One of the key results of this study was that the curing temperature for the coating dramatically affected both the coating spalling area fraction, f _S, and the manner in which the crack spacing changed as a function of the applied indentation load.     

采用通用有限元程序的弥散裂缝模型和分层壳单元模拟钢筋混凝土构件裂缝宽度

该文基于弥散裂缝模型,采用通用有限元程序的分层壳单元计算钢筋混凝土构件裂缝宽度的方法。讨论了理论基础,Bazant和Oh提出的经典裂缝带理论主要针对素混凝土构件,严重的局部化效应导致显著的网格依赖性,而将裂缝带理论拓展到工程常用的配筋混凝土构件时,由于多裂缝分布发展的特点,裂缝带宽应修改为平均裂缝间距而使计算结果与网格无关。在理论基础讨论的基础上,给出了采用通用有限元程序的弥散裂缝模型和分层壳单元计算钢筋混凝土构件裂缝宽度的计算流程,其中,平均裂缝间距将有限元分析中的“应变”概念和工程设计中的“裂缝宽度”概念紧密联系起来,是计算流程中最关键的参数。以某承受负弯矩的简支组合梁混凝土板开裂分析为例,验证并讨论了网格相关性、大软化模量导致数值收敛困难的应对策略、平均裂缝间距的决定性作用等重要问题。     

Statistical study of cracking in reinforced and prestressed concrete members

Abstract

Crack width and crack spacing in concrete flexural members are affected by two parameters, namely, the bond stress between the steel and concrete, and the effective concrete area in tension. This paper presents a statistical study applying dimensional analysis and regression analysis to existing test data to evaluate these two parameters as well as the crack spacing and crack width. It is found that the crack spacing is strongly dependent on the diameter of reinforcing bars and the reinforcement ratio. It is also found that a reduction of steel stress should be considered in calculating the crack width. Based on the results of this study, equations are developed for the calculation of crack width in reinforced and prestressed flexural members.     

Effect of embedded optical fiber sensors on transverse crack spacing of smart composite structures

In this study the effect of the presence of embedded optical fiber sensors on the transverse cracking of cross-ply laminates was investigated. The transverse crack spacing of cross-ply laminates with embedded optical fiber sensors was predicted using modified shear-lag analysis considering the presence of optical fibers and compared with experimental results. The effect of the orientation and quantity of optical fibers was evaluated and the effect of the coating of optical fiber was also investigated. Specimens were made with transparent glass/epoxy prepreg because the transverse crack and other damages such as delamination, splitting and bleeding of laser can be examined directly and visually. It has been found that the transverse crack spacing was not affected significantly by the embedding of optical fibers at low volume fraction of optical fibers. However, the cracks of specimens with embedded optical fibers which were initiated at a slightly lower stress level showed smaller spacing at the same stress level than those of specimens without embedded optical fibers. The theoretical crack spacing evaluated from the shear lag analysis showed good agreements with experimental results.     

Film cracking and debonding in a coated fiber

A fracture mechanics based methodology for the determination of interface fracture toughness from crack spacing in a thin coated fiber is presented. The coating (film) may be regarded as the matrix material in typical experiments employing this configuration. Matrix crack spacing is considered to be the result of a competitive process between matrix segmentation and interface debonding which are assumed to be governed by critical energy release rate criteria. Matrix cracks are assumed to form by the process of channeling in the circumferential direction and steady state conditions are assumed at the matrix crack front in the channeling direction. Energy release rates are determined using domain integral procedures in conjunction with the finite element method. The minimum crack spacing is obtained as a function of applied stress for different values of interface fracture toughness. A methodology to relate the saturated crack spacing to interface fracture toughness is developed. Interfaces are classified into three categories: weak, intermediate and strong. It is shown that in experiments of this type, quantitative information about the interface fracture toughness can be obtained for intermediate interfaces while qualitative information may be obtained for weak and strong interfaces.     

Characterization of the failure behavior of zinc coating on dual phase steel under tensile deformation

The failure behavior of hot-dip galvanized zinc coatings on dual phase steels under tensile deformation is characterized with in situ scanning electron microscopy (SEM). Under tension, the pre-existed microcracks and voids at the zinc grain boundaries propagate along the zinc grain boundaries to form crack nets within the coating, leading to a segmented fracture of the zinc coating with the crack spacing approximately equal to the zinc grain size. With further loading, the coating segments partially delaminated along the interface between the top zinc layer and the inhibition layer instead of the interface between the inhibition layer and steel substrate. As the c-axis of zinc grains trends to be normal to the tensile loading direction, the twinning deformation became more noticeable, and meanwhile the coating delamination was diminished. The transverse and incline tunneling cracks occurred in the inhibition layer with tensile deformation. The existence of the brittle FeZn₁₃ particles on top of the inhibition layer was unfavorable to the coating adhesion.     

Modeling a fracture set in a layered brittle material

A new fracture experimental technique using a brittle coating on PMMA substrates for mode I fractures in layered brittle materials is introduced in this paper. Different strain histories can be applied to the coating including constant strain (relaxation), strain cycling, strain magnitude, and strain rate. Fracture parameters, number of cracks, length of crack, spacing, spatial density, and propagation velocity describe the state of a fracture set.     

On the interaction of channeling/segmentation cracks of coating: Study on the critical spacing

Channeling/segmentation cracks may arise in the coating subjected to in-plane tensile stress. The interaction between these multiple cracks, say the effect of the spacing between two adjacent cracks on the behaviors of channels themselves and the interface around the interface corners, attracts wide interest. However, if the spacing is greater than a specific magnitude, namely the Critical Spacing (CS), there should be no interaction between such channeling/segmentation cracks. In this study, the mechanism of the effect of the crack spacing on the interfacial stress around the interface corner will be interpreted firstly. Then the existence of the CS will be verified and the relationship between the CS and the so-called stress transfer length in coating will be established for plane strain condition. Finally the dependence of the stress transfer length, simultaneously of the CS, on the sensitive parameters will be investigated with finite element method and expressed with a simple empirical formula.     

Spherical indentation and scratch durability studies of transparent conducting layers on polymer substrates

The effect of moderate normal and tangential spherical loading on the durability of brittle ceramic films sputtered on polymer substrates is investigated. Indium tin oxide films with various thicknesses are deposited by sputtering on polyethylene terephthalate substrates and their mechanical durability is assessed using a spherical nanoindenter and scratch tester with built-in optical microscopy capability.It is observed that crack initiation occurs at 40 mN normal applied load. As loading increases, formation of brittle ring cracking and of secondary radial cracks is evident. It is also shown that ring crack spacing is thickness dependent. During scratch testing two main coating failure modes are observed. The first is through thickness cracking and the second is buckling spallation of the coating. Both failure mechanisms exhibit thickness dependence.     

基于荷载长期效应RAC梁裂缝宽度计算方法研究

通过对不同取代率时再生混凝土(RAC)梁裂缝宽度进行长期加载试验研究, 分析了短长期荷载作用下正截面裂缝随时间变化而发展的规律. 研究表明:长期荷载作用下, 再生混凝土裂缝较普通混凝土的快增长时期出现显著“后延”特点, 且增长期持续时间变长. 以试验结果为依据, 拟合回归出内力臂系数、平均裂缝间距、钢筋应变不均匀系数计算公式, 建立了以综合法为理论基础的短期裂缝最大宽度计算公式, 通过多方数据校核满足计算精度, 结合长期裂缝宽度附加时变系数, 提出不同取代率时再生混凝土梁最大裂缝宽度计算公式.     

钢筋钢纤维自密实混凝土梁裂缝宽度试验研究

通过9根钢筋钢纤维自密实混凝土梁的四点弯曲试验,分析了钢纤维体积率、配筋率对钢筋钢纤维自密实混凝土梁裂缝形态、裂缝宽度以及裂缝间距等参数的影响。结果表明:在自密实混凝土梁中掺加钢纤维可有效限制裂缝的扩展,掺入体积率为0.38%和0.64%的钢纤维,可使自密实混凝土梁在正常使用阶段的最大裂缝宽度减小31%~56%,平均裂缝间距减小15%~28%,纵筋应变减小40%~56%。考虑钢纤维在试验梁开裂截面的分布以及应力传递机理,结合试验数据提出了钢筋钢纤维自密实混凝土梁最大裂缝宽度的计算公式,并与MC 2010、RILEM TC-162 TDF及CECS 38:2004的公式进行了对比。计算结果表明:该文建议公式计算的最大裂缝宽度与试验值吻合较好,可用于钢筋钢纤维自密实混凝土梁最大裂缝宽度的分析与验算。     

Validation of stress intensity factors of diametrically opposed corner cracks in a hole

Population of the world’s largest database of stress intensity factor (K) solutions began in 2002 with the calculation of 5.6 million K solutions for diametrically opposed unsymmetric corner cracks at a straight shank hole in a finite width sheet subject to remote tension, remote bending, and bearing loading. Previous work to validate these K solutions was in the form of fatigue life predictions and crack shape development. The current work attempts to build on the previous validation efforts with the addition of comparing the calculated K solutions with K solutions obtained from carefully controlled laboratory experiments. The latter are obtained via fatigue striation measurements at high magnification, up to 40,000×, using a scanning electron microscope and crack growth rate data, in terms of da/dN vs. ΔK at the same test condition. The results show the numerical K solutions are within 20% of the experimentally derived K’s at discrete locations along the crack front. The relatively large error is due to the discontinuous crack extension process of the crack front. Moreover, the entire crack front does not instantaneously extend uniformly in a self similar fashion. The crack extends stepwise over discrete portions of the crack front. Possibly averaging the striation spacing over a specified arc length of the crack front would ameliorate the discontinuous nature of crack propagation resulting in better correlation between the numerical and experimental results. As a result of the current work, we have shown time consuming striation spacing measurements at high magnification are not required to validate K solutions. The best method for such validation efforts is using the fatigue life, crack history, and crack shape which can be obtained at 1/10th the cost of obtaining striation spacing measurements.     

STRESS INTENSITY FACTOR EXPRESSIONS FOR REGULAR CRACK ARRAYS IN PRESSURISED CYLINDERS

Arrays of radial cracks are sometimes observed at the bore of pressurised cylinders. The stress intensity factors of closely spaced regular arrays of edge cracks depends primarily on the crack spacing and are approximately proportional to the square root of crack spacing for crack length to spacing ratios down to 0.16. A stress intensity factor expression for this range of spacing ratios and of engineering accuracy has been developed for a large regular array of radial cracks at the bore of a pressurised cylinde. For smaller spacing ratios the stress intensity factor depends on crack length than crack spacing and a complementary expression has been developed.     

Reduction in energy release rate for mode I fracture of a fibre with a cracked coating layer due to small-scale interfacial debonding

In order to predict the effect of small-scale interfacial debonding on the energy release rate at a crack tip for mode I fracture of a fibre with a cracked coating layer, an approximate calculation method has been presented. The relation of debonding length, thickness of the coating layer and ratio of elastic modulus of the coating layer to that of the fibre, to the energy release rate of the fibre was calculated for some examples. It was demonstrated that small-scale debonding reduces the energy release rate and, therefore, effectively prevents reduction in fibre strength.     

Minimum fatigue striation spacing and its stress amplitude dependence in a commercially pure titanium

We report the fatigue striation spacing of commercially pure titanium with respect to stress amplitude. Rotating bending fatigue tests were performed at 150, 175, 200 and 227 MPa in which samples did not fail at 150 MPa. No fatigue striation up to a certain crack length is observed for the studied conditions. For each condition, a minimum striation spacing value is found that decreases from 0.45 to 0.36 to 0.24 μm with increasing stress from 175 to 200 to 227 MPa, respectively. The minimum striation spacing remains constant up to a certain crack length for each condition. Thereafter, it starts increasing with crack length. It is quite understandable that the constant striation spacing over a certain crack length may not represent the macroscopic fatigue crack growth rate. The fatigue crack growth mechanism during the constant striation spacing region has been discussed in detail.     

预应力铝合金筋嵌入式补强钢筋混凝土梁裂缝分析与计算

完成了7根预应力7075铝合金筋嵌入式补强混凝土梁试件的四点弯曲静载试验,应用非接触式数字图像相关法对混凝土加固梁的裂缝形成、分布、裂缝宽度和间距进行分析,研究了铝合金加固量、预应力以及预应力水平对嵌入式补强混凝土梁试件破坏模式和裂缝特性的影响。试验研究表明:铝合金筋嵌入式补强法可以显著提高混凝土梁的承载能力,施加预应力进一步增强加固梁的强度并延缓混凝土开裂和钢筋屈服;端部锚固有效避免了加固梁试件发生剥离破坏,提高高强铝合金强度利用率;施加预应力、增大加固量和提高预应力水平,均可以有效控制裂缝扩展,减小裂缝宽度和间距;根据中国《混凝土结构设计规范》(GB 50010?2010)对嵌入式非预应力/预应力铝合金筋补强混凝土梁的裂缝宽度和分布进行了计算,理论计算值与试验结果吻合良好,结果表明:中国混凝土结构设计规范给出的正常使用状态下最大裂缝宽度计算方法能够较好地考虑预应力、加固筋数量以及预应力水平对最大裂缝宽度的影响,适用于嵌入式补强钢筋混凝土受弯构件的裂缝计算与分析。     

冷喷涂304不锈钢涂层的弯曲力学行为研究

采用冷喷涂(CGDS)技术在IF钢基体上制备304不锈钢涂层.用SHIMADZU液压伺服疲劳试验机对304不锈钢涂层样品进行三点弯曲实验,用扫描电子显微镜来研究冷喷涂304不锈钢涂层的断裂行为.结果表明:冷喷涂304不锈钢涂层的断裂行为为脆性断裂;裂纹萌生于涂层表面,随着载荷和力矩的增加,裂纹向涂层内部扩展,裂纹在涂层...