Peri-Net-Pro: the neural processes with quantified uncertainty for crack patterns

This paper develops a deep learning tool based on neural processes(NPs)called the Peri-Net-Pro,to predict the crack patterns in a moving disk and classifies them according to the classification modes with quantified uncertainties.In particular,image classification and regression studies are conducted by means of convolutional neural networks(CNNs)and NPs.First,the amount and quality of the data are enhanced by using peridynamics to theoretically compensate for the problems of the finite element method(FEM)in generating crack pattern images.Second,case studies are conducted with the prototype microelastic brittle(PMB),linear peridynamic solid(LPS),and viscoelastic solid(VES)models obtained by using the peridynamic theory.The case studies are performed to classify the images by using CNNs and determine the suitability of the PMB,LBS,and VES models.Finally,a regression analysis is performed on the crack pattern images with NPs to predict the crack patterns.The regression analysis results confirm that the variance decreases when the number of epochs increases by using the NPs.The training results gradually improve,and the variance ranges decrease to less than 0.035.The main finding of this study is that the NPs enable accurate predictions,even with missing or insufficient training data.The results demonstrate that if the context points are set to the 10th,100th,300th,and 784th,the training information is deliberately omitted for the context points of the 10th,100th,and 300th,and the predictions are different when the context points are significantly lower.However,the comparison of the results of the 100th and 784th context points shows that the predicted results are similar because of the Gaussian processes in the NPs.Therefore,if the NPs are employed for training,the missing information of the training data can be supplemented to predict the results.

Crack patterns corresponding to the residual strength plateau of ceramics subjected to thermal shock

The formation strength plateau of ceramics is addressed. A set of of 99A1203 are conducted, mechanism of the residual subjected to thermal shock thermal shock experiments where the thin specimens of 1 mm× 10 mm×50 mm exhibit parallel through edge cracks, and thus permit quantitative measurements of the crack patterns. The cracks evolve with the severity of ther- mal shock. It is found that there is a correlation between the length and density of the thermal shock cracks. The increase of crack length weakens the residual strength, whereas the increase of crack density improves it. In a considerably wide temperature range, the two contrary effects just counteract each other; consequently a plateau appears in the variation curve of the residual strength. A comparison between the numerical and experimental results of the residual strength is made, and they are found in good agreement. This work is helpful to a deep understanding of the thermal shock failure of ceramics.

Surface crack evolution patterns in freeze-thaw damage of fissured rock bodies

To explore the effects of freeze‒thaw cycles on the mechanical properties and crack evolution of fissured sandstone,biaxial compression experiments were carried out on sandstone subjected to freeze‒thaw cycles to characterize the changes in the physical and mechanical properties of fissured sandstone caused by freeze‒thaw cycles.The crack evolution and crack change process on the surface of the fissured sandstone were recorded and analysed in detail via digital image technology(DIC).Numerical simulation was used to reveal the expansion process and damage mode of fine-scale cracks under the action of freeze‒thaw cycles,and the simulation results were compared and analysed with the experimental data to verify the reliability of the numerical model.The results show that the mass loss,porosity,peak stress and elastic modulus all increase with increasing number of freeze‒thaw cycles.With an increase in the number of freeze‒thaw cycles,a substantial change in displacement occurs around the prefabricated cracks,and a stress concentration appears at the crack tip.As new cracks continue to sprout at the tips of the prefabricated cracks until the microcracks gradually penetrate into the main cracks,the displacement cloud becomes obviously discontinuous,and the contours of the displacement field in the crack fracture damage area simply intersect with the prefabricated cracks to form an obvious fracture.The damage patterns of the fractured sandstone after freeze‒thaw cycles clearly differ,forming a symmetrical"L"-shaped damage pattern at zero freeze‒thaw cycles,a symmetrical"V"-shaped damage pattern at 10 freeze‒thaw cycles,and a"V"-shaped damage pattern at 20 freeze‒thaw cycles.After 20 freeze‒thaw cycles,a"V"-shaped destruction pattern and"L"-shaped destruction pattern are formed;after 30 freeze‒thaw cycles,an"N"-shaped destruction pattern is formed.This shows that the failure mode of fractured sandstone gradually becomes more complicated with an increasing number of freeze‒thaw cycles.The effects of freeze‒thaw cycles on the direction and rate of crack propagation are revealed through a temperature‒load coupled model,which provides an important reference for an in-depth understanding of the freeze‒thaw failure mechanisms of fractured rock masses.

Cracking Patterns of Shear Walls in Reinforced Concrete Structure due to Strong Earthquake Based on Mohr-Coulomb Criterion

A primary goal of seismic design of buildings is to protect people's life safety during strong earthquakes. Fundamentally,to predict the survived space and estimate people escape intervals during structural collapse are very important,which requires to describe the failure process more detailedly not only for structural joints but also for slabs and shear walls. In the present paper,the details of Mohr-Coulomb failure criterion with tension-cutoff together with its expression in failure surface and local coordinate system of reinforced concrete( RC) shear wall are given firstly,and then several typical cracking patterns of RC shear wall,such as tension shear crack and compression shear crack, are analyzed based on Mohr-Coulomb failure criterion with tension-cutoff.

A state-of-the-art review of mechanical characteristics and cracking processes of pre-cracked rocks under quasi-static compression

The mechanical characteristics and failure behavior of rocks containing flaws or discontinuities have received wide attention in the field of rock mechanics.When external loads are applied to rock materials,stress-induced cracks would initiate and propagate from the flaws,ultimately leading to the irreversible failure of rocks.To investigate the cracking behavior and the effect of flaw geometries on the mechanical properties of rock materials,a series of samples containing one,two and multiple flaws have been widely investigated in the laboratory.In this paper,the experimental results for pre-cracked rocks under quasistatic compression were systematically reviewed.The progressive failure process of intact rocks is briefly described to reveal the background for experiments on samples with flaws.Then,the nondestructive measurement techniques utilized in experiments,such as acoustic emission(AE),X-ray computed tomography(CT),and digital image correlation(DIC),are summarized.The mechanical characteristics of rocks with different flaw geometries and under different loading conditions,including the geometry of pre-existing flaws,flaw filling condition and confining pressure,are discussed.Furthermore,the cracking process is evaluated from the perspective of crack initiation,coalescence,and failure patterns.

Epitaxial growth and cracking of highly tough 7YSZ splats by thermal spray technology

Thermally sprayed coatings are essentially layered materials and contain large numbers of lamellar pores. It is thus quite necessary to clarify the formation mechanism of lamellar pores which significantly influence coating performances. In the present study, to elaborate the formation mechanism of lamellar pores, the yttria-stabilized zirconia(ZrO_2–7 wt% Y_2O_3, 7YSZ) splats, which have high fracture toughness and tetragonal phase stability, were employed. Interestingly, anomalous epitaxial growth occurred for all deposition temperatures in spite of the extremely high cooling rate,which clearly indicated chemical bonding and complete contact at splat/substrate interface before splat cooling. However, transverse spallation substantially occurred for all deposition temperatures in spite of the high fracture toughness of 7YSZ, which revealed that the lamellar pores were from transverse cracking/spallation due to the large stress during splat cooling. Additionally, fracture mechanics analysis was carried out, and it was found that the stress arose from the constraint effect of the shrinkage of the splat by locally heated substrate with the value about 1.97 GPa. This clearly demonstrated that the stress was indeed large enough to drive transverse cracking/spallation forming lamellar pores during splat cooling. All of these contribute to understanding the essential features of lamellar bonding and further tailoring the coating structures and performance.

Formation of wavy-ring crack in drying droplet of protein solutions

The formations of desiccation cracks and their pattems in drying droplets of protein solutions are studied experimentally. The solvent evaporation causes the dehydration self-organization phenomenon in colloidal droplets, followed by the formations of desiccation cracks. Two categories of highly ordered crack patterns, which we name ＂daisy＂ and ＂wavy-ring＂, are identified in the drying droplets. We explore the shifting of crack patterns from the ＂daisy＂ to the ＂wavy-ring＂ by varying the concentration of protein droplets. The results show that the concentration correlates with the pattern of deposition film directly, and modulates the periodicity of the crack pattern. We investigate the formations and periodicities of these two kinds of crack patterns, and obtain the scaling law of periodicity of the ＂wavy-ring＂ crack pattern. The relationship between the deposition pattern and the highly ordered crack patterns is also examined. This study will help in understanding the formation mechanisms of crack patterns in drying droplets of protein solutions and assist the future design of crack patterns in practical applications.

Pattern transition and sluggish cracking of colloidal droplet deposition with polymer additives

Drying of colloidal droplets often develops versatile depositions.We study the drying deposition of both colloidal droplets containing silica nanoparticles and the silica colloidal droplets with polyethylene oxide(PEO) additives.We focus on the effect of polymer additives on the deposition formation and the cracking dynamics by using in-situ microscope observation.With PEO additives,a transition from ring-like deposition to uniform deposition is observed,and the cracking dynamics is greatly reduced.The PEO additives enhance the adsorption of particles at the air-water interface,thus forming the network structure at the interface which blocks the outward capillary flow.This contributes to the uniform deposition.Meanwhile,the multi-distribution of the aggregates size enhances the non-homogeneity of the drying film and consequently results in multi-nucleation of cracks.This reduces the stress accumulation that drives the crack propagation and may be responsible for the sluggish cracking dynamics.

Stable and realistic crack pattern generation using a cracking node method

This paper presents a method for simulating surface crack patterns appearing in ceramic glaze, glass, wood and mud. It uses a physically and heuristically combined method to model this type of crack pattern. A stress field is defined heuristically over the triangle mesh of an object. Then, a first-order quasi-static cracking node method （CNM） is used to model deformation. A novel combined stress and energy combined crack criterion is employed to address crack initiation and propagation separately according to physics. Meanwhile, a highest-stress-first rule is applied in crack initiation, and a breadth-first rule is applied in crack propagation. Finally, a local stress relaxation step is employed to evolve the stress field and avoid shattering artifacts. Other related issues are also discussed, such as the elimination of quadra- ture sub-cells, the prevention of parallel cracks and spurious crack procession. Using this method, a variety of crack patterns observed in the real world can be reproduced by changing a set of parameters. Consequently, our method is robust because the computational mesh is independent of dynamic cracks and has no sliver elements. We evaluate the realism of our results by comparing them with photographs of realworld examples. Further, we demonstrate the controllability of our method by varying different parameters.

Shrinkage Characteristics of Lime Concretion Black Soil as Affected by Biochar Amendment

Studies have reported that biochar is a sustainable amendment that improves the chemical and physical properties of soil.In this study,an incubation experiment was conducted to investigate the effects of different application rates of biochar on the cracking pattern and shrinkage characteristics of lime concretion black soil after three wetting and drying cycles.Biochar derived from the corn straw and peanut shell mixture was applied to the soil at rates of 0,50,100,and 150 g kg^(-1)dry weight,representing the treatments T_(0),T_(50),T_(100),and T_(150),respectively.During the wetting and drying cycles,the cracking pattern and shrinkage characteristics of the unamended and amended soil samples were recorded.Application of biochar significantly increased soil organic carbon content in the samples.During soil desiccation,biochar significantly reduced the rate of water loss.Cracks propagated slowly and stopped due to the relatively higher water content in the soil applied with biochar.The cracking area density(ρ_c),equivalent width,fractal dimension,and cracking connectivity index decreased during the drying process with increasing application rate of biochar.Theρ_(c )value of the T_(50),T_(100),and T_(150) treatments decreased by 33.6%,52.1%,and 56.9%,respectively,after three wetting and drying cycles,whereas the T_(0) treatment exhibited a marginal change.The coefficient of linear extensibility,an index used to describe onedimentional shrinkage,of the unamended soil sample(T_(0))was approximately 0.23.Application of 100 and 150 g kg^(-1)biochar to the soil significantly reduced the shrinkage capacity by 41.45%and 45.54%,respectively.The slope of the shrinkage characteristics curve,which indicates the ralationship between soil void ratio and moisture ratio,decreased with increase in the application rate of biochar.Furthermore,compared with the T_(0) treatment,the proportional shrinkage zone of the shrinkage characteristic curve of the T_(50),T_(100),and T_(150) treatments decreased by 5.8%,13.1%,and 12.1%,respectively.Differences were not observed in the moisture ratio at the maximum curvature of the shrinkage characteristic curve among the treatments.The results indicate that biochar can alter the cracking pattern and shrinkage characteristics of lime concretion black soil.However,the effects of biochar on the shrinkage of lime concretion black soil are dependent on the number of wetting and drying cycles.

DETERMINATION OF FRACTURE TOUGHNESS OF BRITTLE MATERIALS BY INDENTATION

Fracture toughness is one of the crucial mechanical properties of brittle materials such as glasses and ceramics which demonstrate catastrophic failure modes. Conventional stan- dardized testing methods adopted for fracture toughness determination require large specimens to satisfy the plane strain condition. As for small specimens, indentation is a popular, sometimes exclusive testing mode to determine fracture toughness for it can be performed on a small flat area of the specimen surface. This review focuses on the development of indentation fracture theories and the representative testing methods. Cracking pattern dependent on indenter geometry and material property plays an important role in modeling, and is the main reason for the diversity of indentation fracture theories and testing methods. Along with the simplicity of specimen require- ment is the complexity of modeling and analysis which accounts for the semi-empirical features of indentation fracture tests. Some unresolved issues shaping the gap between indentation fracture tests and standardization are also discussed.

Blast response of full-size concrete walls with chemically reactive enamel （CRE）-coated steel reinforcement

In this study, two full-size concrete wails were tested and analyzed to demonstrate the effectiveness of a chemically reactive enamel （CRE） coating in improving their mechanical behavior under blast loading： one with CRE-coated rebar and the other with uncoated rebar. Each wall was subjected in sequence to four explosive loads with equivalent 2, 4, 6-trinitrotoluene （TNT） charge weights of 1.82, 4.54, 13.6, and 20.4 kg. A finite element model of each wall under a close-in blast load was developed and validated with pressure and strain measurements, and used to predict rebar stresses and concrete surface sWain distributions of the wall. The test results and visual inspections consistently indicated that, compared with the barrier wall with uncoated reinforcement, the wall with CRE-coated rebar has fewer concrete cracks on the front and back faces, more effective stress transfers from concrete to steel rebar, and stronger connections with its concrete base. The concrete surface strain distributions predicted by the model under various loading conditions are in good agreement with the crack patterns observed during the tests.

Flexural Behavior of Cross-Connected Brick Masonry Infill Wall Panels Supported on Reinforced Concrete Beam Grids

This paper presents an experimental investigation on the flexural behavior of cross-connected brick masonry infill wall panels supported on reinforced concrete beam grids above and below the walls.The experimental program was comprised of six wall systems.The effect of change in lower beam stiffness relative to the wall and the geometry of the main walls were investigated.From the results of the experimental tests,the increase in the depth of the lower beam grid reduces the deflection,resulting in an increase in the load carrying capacity of the wall.Further,the stiffness of the main walls affects the deflection and the failure load of the cross walls.