Crack Damage Research Articles

Multiscale fracture, physical and mechanical properties of stromboli volcano (Italy) edifice

The physical, mechanical and fracture properties at Stromboli volcano have been integrated at multiple scales to understand whether the interplay between a presumed NE/SW rift zone and the Sciara del Fuoco (SDF) depression has resulted in a zone of weakness able to promote fracturing prone to flank instability. Multiscale fracture quantification by imaging via FracPaQ toolbox both fractures and sample scale fractures has been integrated with rock physics and rock mechanics experiments on cm-scale samples belonging to the Paleostromboli, Vancori, Neostromboli, Pizzo and Present Deposit volcanic cycles that have been taken from within and outside the rift zone. The structural changes to the edifice have been quantitively assessed by mapping at different scale fracture properties such density and orientation within and outside the rift zone allowing to identify the potential damaged zones that could reduce the edifice strength.Results indicate that basalt textures, microfracture density, porosity, chemical zoning and preferential alignments, despite lithologically dependent, can be related to the NE/SW zone of weakness at the regional scale and to collapsed volumes that have been subject to continuous intrusive activity. Numerical inversion models have been performed to cross correlate fracture density in the basalts at multiple scales.A link between microfracture density and seismic velocities has been also established via numerical modelling, allowing to interpret in terms of degree of fracturing the results of seismic tomographies at the field scale, providing a novel method to image crack damage evolution within the inner structure of the volcano edifice.

Vison Transformer-Based Automatic Crack Detection on Dam Surface

Dam is an essential structure in hydraulic engineering, and its surface cracks pose significant threats to its integrity, impermeability, and durability. Automated crack detection methods based on computer vision offer substantial advantages over manual approaches with regard to efficiency, objectivity and precision. However, current methods face challenges such as misidentification, discontinuity, and loss of details when analyzing real-world dam crack images. These images often exhibit characteristics such as low contrast, complex backgrounds, and diverse crack morphologies. To address the above challenges, this paper presents a pure Vision Transformer (ViT)-based dam crack segmentation network (DCST-net). The DCST-net utilizes an improved Swin Transformer (SwinT) block as the fundamental block for enhancing the long-range dependencies within a SegNet-like encoder–decoder structure. Additionally, we employ a weighted attention block to facilitate side fusion between the symmetric pair of encoder and decoder in each stage to sharpen the edge of crack. To demonstrate the superior performance of our proposed method, six semantic segmentation models have been trained and tested on both a self-built dam crack dataset and two publicly available datasets. Comparison results indicate that our proposed model outperforms the mainstream methods in terms of visualization and most evaluation metrics, highlighting its potential for practical application in dam safety inspection and maintenance.

Analysis of Microwave-Induced Damage in Granite Aggregates Influenced by Mineral Texture

The use of microwave energy to recycle high-quality coarse aggregates from waste concrete or assist hard rock breakage in underground building engineering is promising. Controlling or promoting the damage of coarse aggregates, i.e., hard rocks, under microwave irradiation is a crucial issue faced by these techniques. Understanding the damage mechanisms of hard rocks exposed to microwaves is thus urgent. Fracture toughness is a significant mechanical parameter of rocks that reflects their ability to resist crack propagation and damage evolution. In this study, the fracture toughness degradation of microwave-heated granite was investigated by combining experimental investigations and numerical simulations. A three-point-bending (TPB) experiment was conducted on granite specimens after microwave irradiation. A coupled electromagnetic–thermal–mechanical model considering the actual mineral texture of the granite specimen was established. The evolution of the temperature gradient and stress field near the initial notch tip were investigated. The results suggest that the microwave-induced maximum temperature gradient and stress in granite are at the plagioclase–quartz (Pl–Qtz) interfaces or inside the Pl near the boundary. The region of cracking initiation was defined as the damage zone, which could be obtained by comparing the microwave-induced thermal stress with the critical value. The fracture toughness degradation, which corresponds to the evolution of the damage zones, can be divided into two stages. A relatively rapid decrease in fracture toughness in the first stage is primarily caused by the spread of the scattered damage zones along the Pl–Qtz interfaces; subsequently, a gentler fracture toughness degradation results mainly from the extension of the previous damage zones.

Tension and Shear Behaviour of Basalt Fiber Bio-Composites with Digital Image Correlation and Acoustic Emission Monitoring.

This research investigates the mechanical behavior and damage evolution in cross-ply basalt fiber composites subjected to different loading modes. A modified Arcan rig for simultaneous acoustic emission (AE) monitoring was designed and manufactured to apply quasi-isotropic shear, combined tensile and shear loading, and pure tensile loading on specimens with a central notch. Digital image correlation (DIC) was applied for high-resolution strain measurements. The measured failure strengths of the bio-composite specimens under different loading angles are presented. The different competing failure mechanisms that contribute to the local reduction in stress concentration are described. Different damage mechanisms trigger elastic waves in the composite, with distinct AE signatures that closely follow the sequence of fracture mechanisms. AE monitoring is employed to capture signals associated with structural damage initiation and progression. The characteristic parameters of AE signals are correlated with crack modes and damage mechanisms. The evolution of AE parameters during the peak load transition is presented, which enables the timely AE detection of the maximum load transition. The combination of DIC and AE monitoring improves understanding of the mechanical response and failure mechanisms in cross-ply basalt fiber composites, offering valuable insights for possible performance monitoring and structural reliability in diverse engineering applications.

Physical and mechanical characteristics deterioration and crack evolution of sandy mudstone in an open-pit mine under multiple freeze–thaw cycles

In open-pit mines located in cold regions north of the 38°N latitude, there are significant freeze–thaw phenomena in slope rocks. This study conducted freeze–thaw cycle tests, considering the number of freeze–thaw cycles and the freezing temperature, on sandy mudstone commonly found in the slopes of open-pit mines. The investigation focused on the effects of freeze–thaw cycles on the physical and mechanical properties and acoustic emission (AE) characteristics of sandy mudstone. The results show that, with an increase in the number of freeze–thaw cycles and a decrease in freezing temperature, the sandy mudstone specimens exhibit nonlinear exponential changes in mass loss rate, P-wave velocity loss rate, peak strain, uniaxial compressive strength (UCS) and elastic modulus, and the amplitude of these changes gradually decreases. The stress–strain curves of specimens shift gradually from apparently brittle to plastic. Simultaneously, the microstructure changes from dense to loose, the micro surface transitions from flat to rough, and cracks and pore defects gradually develop. The peak AE ringing counts, cumulative AE ringing counts, crack initiation stress, and crack damage stress of the specimens all decrease with an increase in the number of freeze–thaw cycles and a decrease in freezing temperature. This suggests a shift from brittle failure to ductile failure. However, the ratio of crack initiation stress and crack damage stress to peak stress does not vary significantly with the number of freeze–thaw cycles and freezing temperature.

Crack detection and damage evaluation of asymmetrical steel-reinforced concrete frame nodes using acoustic emission technology

ABSTRACT Detecting cracks in steel-reinforced concrete (SRC) frame nodes is crucial for ensuring structural safety. This study employs acoustic emission (AE) technology to monitor the growth of concrete structural defects in real time. The aim is to establish a sensitive assessment method based on AE parameters to accurately assess the damage stages of SRC frame nodes by considering the complex crack extension mechanism in SRC structures. An experimental study of the AE characteristics of SRC frame nodes under low-cycle loading was performed. The crack evolution process of SRC frame nodes was monitored and analysed using the AE parameters. The results showed that ringing count is the AE parameter more sensitive to the damage of the SRC frame node. The damage evaluation method was established based on the variation coefficient analysis of the AE parameters. Considering the sudden change in the growth rate of the damage index, the damage evolution process of the SRC frame nodes can be accurately divided into three stages: initial crack compaction, rapid crack expansion, and crack penetration. These stages are consistent with the mechanical properties of SRC frame nodes.

Study on the mechanical properties and microstructure of recycled concrete reinforced with basalt fibers and nano-silica in early low-temperature environments

Abstract The effects of basalt fibers (BF) and nano-silica (NS) on the mechanical properties and microstructure of recycled concrete (RC) in early low-temperature environments were investigated by placing the BF and NS modified RC specimens in the environments of −20, −10, 0, and 25°C for curing for 6 h, followed by standardized maintenance. The damage morphology and mechanical properties of modified RC were analyzed in such environments. The formulae for the compressive strength of RC, which was affected by BF and NS, were fitted using statistical product and service solutions, and a micromorphological analysis of the modified RC was conducted using scanning electron microscope. The mechanical properties of RC decreased owing to the influence of early low temperatures, among which 0°C caused the largest damage crack and the most serious effects. In the early low-temperature environments, the physical properties of RC generally increased and then decreased with the increase in BF dosage; however, increasing NS dosages improved its mechanical properties. The composite doping of BF and NS was more obvious than the single doping of BF or NS to enhance the performance of RC, and the internal pore structure was considerably improved. The preferred doping amounts were 3 kg m−3 of BF and 2% NS.

Quantitative Analysis and 3D Visualization of Crack Behavior in 3D-Printed Rock-Like Specimens with Single Flaw Using In-Situ Micro-CT Imaging

3D printing technology allows for precise control of preparing complex geometries and internal defects in printed rock analogs, while in-situ Micro-CT imaging enables real-time observation of crack behavior. The combination of these technologies offers a new research approach for studying rock crack behavior. In this study, 3D-printed rock-like specimens containing a pre-existing flaw were prepared using a gypsum powder-based 3D printer. An advanced in-situ Micro-CT system equipped with a loading device was used to quantitatively and visually investigate the crack behavior in 3D-printed specimens under uniaxial compression testing. 2D CT images obtained from in-situ compression testing at different deformations could be used to reconstruct a 3D model and visually identify the crack patterns of the extracted cracks in 3D-printed specimens. The initiation angle of cracks, volume of the pre-existing flaw, volume of newly formed cracks, and damage value with respect to strains were analyzed to quantitatively investigate crack behavior. The results indicated that within the 3D-printed specimens, tensile cracks were first initiated near the internal flaw, followed by the occurrence of shear cracks or tensile-shear mixed cracks at the flaw tips. Additionally, there was a negative linear correlation between the initiation angle of newly formed cracks and the initial flaw angle. For flaw angles in the range of 0° ≤ α ≤ 45°, a higher number of newly formed cracks were observed in the 3D-printed specimens, and the rates of increase in crack volume and damage values with strain were faster. However, for flaw angles in the range of 45° < α ≤ 90°, the results showed the opposite trend. Furthermore, through comparison with the crack behavior of natural rocks containing a single flaw, it was found that the failure modes and crack behavior of the 3D-printed specimens exhibit certain similarities with natural rocks.

A New Rock Brittleness Index Based on Crack Initiation and Crack Damage Stress Thresholds

A New Rock Brittleness Index Based on Crack Initiation and Crack Damage Stress Thresholds

Recycling of copper tailing as filler material in asphalt paving mastic: A sustainable solution for mining waste recovery

Copper tailings are a category of solid waste discharged after the beneficiation process in mining plants. The significant concern raising stringent environmental issues give impetus to explore the multi-channel utilization of copper tailings in a sustainable manner. Concerning the fact that no study has systematically compared properties of copper tailings filled (CTP) asphalt mastic with conventional limestone filler mastic (LP) at different filler-to-asphalt ratios, multiscale and multi-dimensional comparisons between the characteristics of CTP-asphalt and LP-asphalt mastics were made in this study to thoroughly explore the feasibility and potential of recycling CTP as alternative filler in asphalt materials. Four ratios from 0.3 to 1.2 were used to manufacture asphalt mastics. The in-service pavement performance of asphalt mastics including resistances to rutting, low-temperature cracking and moisture damage was explored. Finally, the environmental and economic perspectives regarding the recycling of copper tailings are analyzed. Results indicate that CTP possesses a rougher surface, a larger specific surface area, and a more uniform pore size distribution than LP, particularly across the mesopores range. These characteristics could promote the adsorption of asphalt on its particle surface, potentially leading to enhanced filler-particle interaction. Regarding pavement performance, CTP-asphalt mastic outperforms LP-asphalt mastic in terms of high-temperature performance. Meanwhile, its low-temperature performance and moisture stability are only limitedly declined with the acceptable performance. Further, heavy metals leaching tests suggest that the risk for the substantial utilization of CTP in paving asphalt is absent. The related outcomes have verified the promising potential of CTP as an alternative candidate to substitute the conventional filler in paving asphalt from comprehensive consideration of in-service performance, and environmental and economic benefits.

CNN-Transformer hybrid network for concrete dam crack patrol inspection

Regular patrol inspection of concrete dams can detect cracks at an early stage. However, conventional crack segmentation models based on deep learning (DL) are difficult to be deployed in resource-constrained mobile devices due to the large number of parameters. This paper describes a lightweight semantic segmentation model, termed as CrackTrNet, for images of concrete dam cracks. CrackTrNet is a hybrid U-shaped model based on convolutional neural network (CNN) and Vision Transformer. The CNN is adopted to extract low-level visual features and the Transformer focuses on learning the global contextual information. The results demonstrate that its segmentation accuracy can reach 97.60%, while the model size is only 34.86 MB, which is 66.12%–87.85% lower than that of current mainstream DL-based models. To make the model more practical, a crack inspection mobile application (APP) is developed using Android Studio. The integration of lightweight CrackTrNet and APP can effectively assist the intelligent inspection of dam cracks to ensure structural safety.

Underwater dam crack image generation based on unsupervised image-to-image translation

Underwater crack detection is necessary for the safe operation of concrete dams. Current deep-learning-based underwater crack detection methods rely heavily on a large number of crack images; these images are difficult to collect because of complex and dangerous underwater environments. This study proposes a method that can generate underwater dam crack images using above-water dam crack images through an image-to-image translation method. CycleGAN, which is more powerful than other models, was optimized to generate underwater dam crack images by translating existing above-water dam crack images into underwater styles. The generated underwater images were validated using the following major computer vision tasks: classification, object detection, and semantic segmentation. The results demonstrate the potential of these generated images for training and optimizing deep-learning-based crack-detection methods. This method is expected to solve the problem of insufficient data and enhance deep-learning-based detection networks.

Delamination and crack detection and localization of a laminated composite plate structure using regression and regression-based neural network methods

Despite significant progress, a comprehensive analysis of Machine learning algorithms for detecting delamination and crack damage in composite laminate plates is noticeably absent in the literature. This study aims to bridge this gap by meticulously help spectrum of six regression algorithms. By utilizing simulated displacement-time responses from a 16-layer laminated composite plate structure subjected to a random force, a robust dataset is constructed to evaluate the efficacy of these machine learning paradigms. Performance assessments rely on critical metrics: coefficient of determination (R2), mean absolute error (MAE), root mean squared error (RMSE), and mean absolute percentage error (MAPE).

Interface cracking damage of W/Cu monoblocks as divertor target after high-cyclic plasma discharges in EAST

W/Cu monoblocks will be employed in ITER as divertor targets for high heat loads. Experimental results of W/Cu monoblocks in high heat flux (HHF) tests have demonstrated their endurance on 5000 cycles at 10 MW/m2 and occasionally 300 cycles at 20 MW/m2. However, plasma-facing units (PFUs) serve in a harsh and complex environment in tokamaks and whether W/Cu monoblocks can show the same excellent properties in tokamaks needs to be further tested. Experimentally evaluating the evolution of ITER-like PFUs is one of the main missions for the EAST tokamak. The ITER-like actively cooled W/Cu monoblocks installed in the EAST lower divertor in 2021 exhibited abnormal behavior after 13,346 plasma discharges. The abnormal temperature evolution of the component was observed via infrared cameras (IR). Subsequent non-destructive testing (NDT) indicated that it might primarily arise from interface damage and scanning electron microscopy (SEM) confirmed that there were obvious cracks at the interface. The cracking center was also found above the interface. Simulation of the structural characteristics of W/Cu monoblocks under heat load in EAST can obtain temperature distribution and stress–strain distribution, which can be used to analyze the causes of material interface cracks. These findings unveil the phenomenon and mechanism of interface damage in W/Cu monoblocks after enduring over 10,000 plasma discharges in EAST, providing valuable insights for the future long-term application of W/Cu monoblocks in ITER and fusion reactors.

Crack propagation and damage evolution of metallic cylindrical shells under internal explosive loading

This paper investigates the three-dimensional crack propagation and damage evolution process of metallic column shells under internal explosive loading. The calibration of four typical failure parameters for 40CrMnSiB steel was conducted through experiments and subsequently applied to simulations. The numerical simulation results employing the four failure criteria were compared with the differences and similarities observed in freeze-recovery tests and ultra-high-speed tests. This analysis addressed the critical issue of determining failure criteria for the fracture of a metal shell under internal explosive loads. Building upon this foundation, the damage parameter Dc, linked to the cumulative crack density, was defined based on the evolution characteristics of a substantial number of cracks. The relationship between the damage parameter and crack velocity over time was established, and the influence of the internal central pressure on the damage parameter and crack velocity was investigated. Variations in the fracture modes were found under different failure criteria, with the principal strain failure criterion proving to be the most effective for simulating 3D crack propagation in a pure shear fracture mode. Through statistical analysis of the shell penetration fracture radius data, it was determined that the fracture radius remained essentially constant during the crack evolution process and could be considered a constant. The propagation velocity of axial cracks ranged between 5300 m/s and 12600 m/s, surpassing the Rayleigh wave velocity of the shell material and decreasing linearly with time. The increase in shell damage exhibited an initial rapid phase, followed by deceleration, demonstrating accelerated damage during the propagation stage of the blast wave and decelerated damage after the arrival of the rarefaction wave. This study provides an effective approach for investigating crack propagation and damage evolution. The derived crack propagation and damage evolution law serves as a valuable reference for the development of crack velocity theory and the construction of shell damage evolution modes.

Deep learning-based three-dimensional crack damage detection method using point clouds without color information

Automated high-precision crack detection on building structures under poor lighting conditions poses a significant challenge for traditional image-based methods. Overcoming this challenge is crucial to enhance the practical applicability of structural health monitoring and rapid damage assessment, especially in post-disaster scenarios like earthquakes. To address this challenge, this paper presents a deep learning-based three-dimensional crack detection method that utilizes light detection and ranging (LiDAR) point cloud data. Our method is specifically designed to address crack detection without relying on color information input, resulting in high-precision and robust apparent damage detection. The key contribution of this paper is the NL-3DCrack model, which enables automated three-dimensional crack semantic segmentation. This model comprises a feature embedding module, an incomplete neighbor feature extraction module, a decoder, and morphological filtering. Notably, we introduce an innovative incomplete neighbor mechanism to effectively mitigate the impact of outliers. To validate the effectiveness of our proposed method, we establish two three-dimensional crack detection datasets, namely the Luding dataset and the terrestrial laser scanner dataset, which are based on earthquake disasters. Experimental results demonstrate that our method achieves remarkable performance, with an intersection-over-union of 39.62% and 51.33% on the respective test sets, surpassing existing point cloud-based semantic segmentation models. Ablation experiments further confirm the effectiveness of our approach. In summary, our method showcases exceptional crack detection performance on LiDAR data using only XYZI channels. With its high precision and reliable results, it offers significant utility in real-world applications, contributing to improved structural health monitoring and rapid damage assessment after disasters, particularly in post-earthquake scenarios.

Numerical simulation of rock blasting under different in-situ stresses and joint conditions.

High primary rock stress can limit the generation of rock cracks caused by blasting, and blasting usually shows different rock breaking states under different primary rock stress conditions. There are a large number of naturally formed joints in rock mass, due to the limitations of laboratory tests, a numerical model of jointed rock mass was established using LS-DYNA software to investigate the evolution of blasting damage under various in-situ stresses and open joints. In this simulation, using the Lagrange-Euler (ALE) procedure and the equation of state (JWL) that defines explosive materials, the study considered different joint thicknesses (2cm, 4cm, and 6cm), joint angles (0°, 30°, 60°, and 90°), and in-situ stress conditions (lateral stress coefficients of 0.5, 1, and 2, with vertical in-situ stresses of 10MPa and 20MPa), through stress analysis and damage area comparison, the relationship between damage crack propagation and horizontal and vertical stress difference is explored. The research aimed to understand the mechanisms underlying crack initiation and propagation. The results show that: (1) The presence of joints exerts a barrier effect on the expansion and penetration of cracks. When explosion stress waves reach the joint surface, their propagation is impeded, leading to the diffusion of wing cracks at the joint ends. When the lateral stress coefficient and joint angle are the same, an increase in initial in-situ stress results in a reduction in the area of the blasting damage zone. (2) Under the same initial in-situ stress conditions, the area of the blasting damage zone initially increases and then decreases with an increasing joint angle. However, it remains larger than that without a joint, and there exists an optimal angle that maximizes the damage area. In the simulated conditions, the area of damage cracks is greatest when the joint angle is 60° dip angle. (3) The presence of initial in-situ stress has a certain impact on the initiation and expansion of blasting cracks. The degree and nature of this influence are not solely related to the lateral stress coefficient but also depend on the joint's angle and thickness. When in-situ stress is present, the initial in-situ stress field's pressure is not conducive to the initiation and propagation of blasting cracks. However, the existence of a joint has a noticeable guiding and promoting effect on crack propagation, and the pattern of crack propagation is influenced by both joint and in-situ stress conditions.

Dynamic compressive properties of UHPC under one-dimensional stress wave: The influence of steel fiber morphology and curing regime

The low matrix strength and insufficient toughness of conventional concrete structures seriously threaten the service performance when subjected to intensive compressive waves. This study aims to comprehensively investigate the impact of steel fiber morphology and curing regime on the dynamic compressive properties of Ultra-high performance concrete (UHPC) under one-dimensional stress wave. Seeking to improve its impact resistance without changing the mix ratio. Three steel fiber types (straight, wave, hooked) and two curing regimes (steam at 90 °C, dry heat at 180 °C) were selected as experimental variables. Quasi-static mechanical properties of UHPC were initially calibrated, followed by dynamic compressive tests utilizing the Split Hopkinson Pressure Bar (SHPB) system. The compressive stress-strain relationships and corresponding dynamic mechanical parameters of six types of UHPC were calculated under five impact velocities (8.5 m/s, 10.8 m/s, 13.1 m/s, 15.2 m/s, 17.3 m/s). Furthermore, the dynamic failure mode and evolutionary process of UHPC under high-speed impact was meticulously captured by a high-speed camera. CT scanning was utilized to observe the crack propagation path and damage patterns under low strain rate. Finally, SEM and EDS testing was conducted to unravel the underlying mechanisms of the curing regime and fiber morphology on the dynamic compressive properties of UHPC. The recalibrated empirical DIFfc model suitable for UHPC under strain rates of 37 s-1 to 212 s-1 was proposed.

Identification of the Surface Cracks of Concrete Based on ResNet-18 Depth Residual Network

To ensure the safety and durability of concrete structures, timely detection and classification of concrete cracks using a low-cost and high-efficiency method is necessary. In this study, a concrete surface crack damage detection method based on the ResNet-18 residual network was developed. This method was implemented by training a model with images to extract the cracks, where the image processing algorithms and deep learning were combined. The results show that the computational accuracy can meet the requirements by utilizing the established image dataset and appropriate model hyperparameters. The trained model had high recognition accuracy when the 256 × 256 resolution images were adopted, and the worst accuracy of crack recognition in the test set was over 90%. The average accuracy in the test set was 91.3% when considering environmental interference generated by processing the images with a brightness adjustment, salt-and-pepper noise, and localized interference. Then, it was demonstrated that the present model possesses good robustness for crack identification in different environments. The average recognition accuracy when dealing with images of a real bridge, which are outside the training dataset, was 99.7%. The residual network model developed in this study has the advantages of low cost, high efficiency, and practicality compared to traditional detection methods. Compared to the existing deep learning methods, the model created in this study requires less computational resources and storage space, and shows a faster training speed and higher accuracy.

Characteristics of 3D Printed Functionally Graded Material for Replacement of Dissimilar Metal Weld in Nuclear Reactor

The dissimilar metal welds in the most of the reactors are connections between low alloy steel parts and stainless steel piping. There is a high possibility of primary water stress corrosion cracking (PWSCC) damage attributed to residual stress caused by the difference in material properties in the dissimilar metal weld joints. A number of accidents such as leakage of radioactive coolant due to PWSCC have been reported around the world, posing a great threat to nuclear safety. The objective of this study is to develop a technology that can fundamentally remove dissimilar metal welds by replacing the existing dissimilar metal parts with the functionally graded material (FGM) manufactured by metal 3D printing consisting of low alloy steel and austenitic stainless steel. A powder production, mixing ratio calculation, and metal 3D printing were performed to fabricate the low alloy steel-stainless steel FGM, and microstructure analysis, mechanical properties, and coefficient of thermal expansion (CTE) measurement of the FGM were performed. As a result, it is observed that CTE tended to increase as the austenite content increased in FGM. The gradual change of coefficient of thermal expansion in a FGM showed that the additive manufacturing using 3D printing was effective for preventing an abrupt change in thermal expansion properties throughout their layers.