COMBINED DAMAGE FRACTURE CRITERIA FOR PIEZOELECTRIC CERAMICS

Mechanical and electrical damages are introduced to study the fracture mechanics of piezoelectric ceramics in this paper. Two kinds of piezoelectric fracture criteria are established using the method of least squares combined with a damage analysis of the well-known piezoelectric fracture experiments of Park and Sun’s. One is based on a linear combination of the mechanical and electrical damages and the other on their nonlinear combination. When the combined damage D is up to its critical value Dc, piezoelectric fracture occurs. It is found from the qualitative comparison of the numerical results with the experimental data that the nonlinearly combined damage fracture criterion can give a better prediction of piezoelectric fracture. And it is concluded from the nonlinearly combined damage fracture criterion that a negative electric feld impedes fracture whereas the efect of a positive electric feld on fracture depends on its magnitude.

A modified 3D mean strain energy density criterion for predicting shale mixed-mode Ⅰ/Ⅲ fracture toughness

The fracture toughness of rocks is a critical fracturing parameter in geo-energy exploitation playing a significant role in fracture mechanics and hydraulic fracturing.The edge-notched disk bending(ENDB)specimens are employed to measure the entire range of mixed-modeⅠ/Ⅲfracture toughness of Longmaxi shale.To theoretically interpret the fracture mechanisms,this research first introduces the detailed derivations of three established fracture criteria.By distinguishing the volumetric and distortional strain energy densities,an improved three-dimensional mean strain energy density(MSED)criterion is proposed.As the critical volumetric to distortional MSED ratio decreases,the transition from tensiondominated fracture to shear-dominated fracture is observed.Our results indicate that both peak load and applied energy increase significantly with the transition from pure mode I(i.e.,tension)to pure modeⅢ(i.e.,torsion or tearing)since mode-Ⅲcracking happens in a twisted manner and mode-Ⅰcracking occurs in a coplanar manner.The macroscopic fracture signatures are consistent with those of triaxial hydraulic fracturing.The average ratio of pure mode-Ⅲfracture toughness to pure mode-Ⅰfracture toughness is 0.68,indicating that the obtained mode-Ⅲfracture resistance for a tensionbased loading system is apparent rather than true.Compared to the three mainstream fracture criteria,the present fracture criterion exhibits greater competitiveness and can successfully evaluate and predict mixed-modeⅠ/Ⅲfracture toughness of distinct materials and loading methods.

Numerical Simulation and Dynamic Fracture Criteria of Thin Cylindrical Shells under Inner Explosive Loading

An FAE (Fuel Air Explosives) device is used to develop a numerical and theoretical analysis of a thin cylindrical shell with inner explosive loading. The dynamic fracture process is simulated numerically in the DYNA3D program using the finite element method. The material’s dynamic properties are described by a strain hardening viscoplastic constitution. A damage variable is introduced in the determination of the dynamic fracture criterion. Final rupture of structure is decided by a rupture strain criterion which is deduced in terms of a critical damage variable. The numerical results have been compared with theoretical solutions.

Modified MK model combined with ductile fracture criterion and its application in warm hydroforming

A modified MK model combined with ductile fracture criterion（DFC-MK model） is proposed to compute the forming limit diagrams（FLDs） of 5A06-O aluminum alloy sheet at different temperatures.The material constant（C） of ductile fracture criterion and initial thickness imperfection parameter（f0） at various temperatures are determined by using a new computing method based on wide sheet bending test.The FLDs at 20 and 200 °C are calculated through the DFC-MK model.The DFC-MK model,which includes the influence of through-thickness normal stress,is written into the subroutine VUMAT embedded in Abaqus/ Explicit.The cylindrical cup hydroforming tests are carried out to verify the model.The results show that compared with experimental observations,the predicted FLDs based on DFC-MK model are more accurate than the conventional MK model;the errors between the simulations and experiments in warm hydroforming are 8.23% at 20 °C and 9.24% at 200 °C,which verify the effectiveness of the proposed model.

On the Characteristics of Rheological Fracture of Rock

Based on the traditional theory of fracture, time dependence of rock fracture is taken into account and the creep fracture criteria are given. The effect of the microcrack zone on fracture toughness is analyzed. Finally, a model for time prediction of rheological fracture is derived and its feasibility is proven.

Numerical evaluation of strength and deformability of fractured rocks

Knowledge of the strength and deformability of fractured rocks is important for design, construction and stability evaluation of slopes, foundations and underground excavations in civil and mining engineering. However, laboratory tests of intact rock samples cannot provide information about the strength and deformation behaviors of fractured rock masses that include many fractures of varying sizes, orientations and locations. On the other hand, large-scale in situ tests of fractured rock masses are economically costly and often not practical in reality at present. Therefore, numerical modeling becomes necessary. Numerical predicting using discrete element methods(DEM) is a suitable approach for such modeling because of their advantages of explicit representations of both fractures system geometry and their constitutive behaviors of fractures, besides that of intact rock matrix. In this study, to generically determine the compressive strength of fractured rock masses, a series of numerical experiments were performed on two-dimensional discrete fracture network models based on the realistic geometrical and mechanical data of fracture systems from feld mapping. We used the UDEC code and a numerical servo-controlled program for controlling the progressive compressive loading process to avoid sudden violent failure of the models. The two loading conditions applied are similar to the standard laboratory testing for intact rock samples in order to check possible differences caused by such loading conditions. Numerical results show that the strength of fractured rocks increases with the increasing confning pressure, and that deformation behavior of fractured rocks follows elasto-plastic model with a trend of strain hardening. The stresses and strains obtained from these numerical experiments were used to ft the well-known Mohr-Coulomb(MC) and Hoek-Brown(H-B) failure criteria, represented by equivalent material properties defning these two criteria. The results show that both criteria can provide fair estimates of the compressive strengths for all tested numerical models. Parameters of the elastic deformability of fractured models during elastic deformation stages were also evaluated, and represented as equivalent Young’s modulus and Poisson’s ratio as functions of lateral confning pressure. It is the frst time that such systematic numerical predicting for strength of fractured rocks was performed considering different loading conditions, with important fndings for different behaviors of fractured rock masses, compared with testing intact rock samples under similar loading conditions.

Experimental Study on Mixed-Mode(Ⅰ–Ⅱ)Fracture Toughness of Freshwater Ice

In recent years,the issue of aircraft icing has gained widespread recognition.The breaking and detachment of dynamic ice can pose a threat to flight safety.However,the shedding and fracture mechanisms of dynamic ice are unclear and cannot meet the engineering needs of ice-shedding hazard assessment.Therefore,studying the fracture toughness of ice bodies has extremely important practical significance.To address this issue,this article uses a centrally cracked Brazilian disk(CCBD)specimen to measure the pure modeⅠtoughness and pure modeⅡfracture toughness of freshwater ice at different loading rates.The mixed-mode(Ⅰ–Ⅱ)fracture characteristics of ice are discussed,and the experimental results are compared and analyzed with the theoretical values of the generalized maximum tangential stress(GMTS)criterion considering the influence of T-stress.The results indicated that as the loading rate increases,the pure modeⅠtoughness and pure modeⅡfracture toughness of freshwater ice decrease,and the fracture toughness of freshwater ice is more sensitive to the loading rate.Ⅰn terms of fracture criteria,the theoretical value of the ratio of pure modeⅡfracture toughness to pure modeⅠfracture toughness based on the GMTS criterion is in good agreement with the experimental value,while the theoretical value based on the maximum tangential stress(MTS)criterion deviates significantly from the experimental value,indicating that the GMTS criterion considering the influence of T-stress can better predict the experimental results.

Discrete Model of Plasticity and Failure of Crystalline Materials

Within the framework of a discrete model of the nuclei of linear and planar defects, the variational principles of sliding in translational and rotational plasticity, fracture by separation (cleavage) and shear (shearing) in crystalline materials are considered. The analysis of mass transfer fluxes near structural kinetic transitions of slip bands into cells, cells into fragments of deformation origin, destruction by separation and shear for fractal spaces using fractional Riemann-Liouville derivatives, local and global criteria of destruction is carried out. One of the possible schemes of the crack initiation and growth mechanism in metals is disclosed. It is shown that the discrete model of plasticity and fracture does not contradict the known dislocation models of fracture and makes it possible to abandon the kinetic concept of thermofluctuation rupture of interatomic bonds at low temperatures.

Dynamic strength of rocks and physical nature of rock strength

Time-dependence of rock deformation and fracturing is often ignored.However,the consideration of the time-dependence is essential to the study of the deformation and fracturing processes of materials,especially for those subject to strong dynamic loadings.In this paper,we investigate the deformation and fracturing of rocks,its physical origin at the microscopic scale,as well as the mechanisms of the time-dependence of rock strength.Using the thermo-activated and macro-viscous mechanisms,we explained the sensitivity of rock strength to strain rate.These mechanisms dominate the rock strength in different ranges of strain rates.It is also shown that a strain-rate dependent Mohr-Coulomb-type constitutive relationship can be used to describe the influence of strain rate on dynamic rock fragmentation.A relationship between the particle sizes of fractured rocks and the strain rate is also proposed.Several time-dependent fracture criteria are discussed,and their intrinsic relations are discussed.Finally,the application of dynamic strength theories is discussed.