Analysis of progressive failure of pillar and instabilitycriterion based on gradient-dependent plasticity

A mechanical model for strain softening pillar is proposed considering the characteristics of progressive shear failure and strain localization. The pillar undergoes elastic, strain softening and slabbing stages. In the elastic stage, vertical compressive stress and deformation at upper end of pillar are uniform, while in the strain softening stage there appears nonuniform due to occurrence of shear bands, leading to the decrease of load-carrying capacity. In addition, the size of failure zone increases in the strain softening stage and reaches its maximum value when slabbing begins. In the latter two stages, the size of elastic core always decreases. In the slabbing stage, the size of failure zone remains a constant and the pillar becomes thinner. Total deformation of the pillar is derived by linearly elastic Hookes law and gradient-dependent plasticity where thickness of localization band is determined according to the characteristic length. Post-peak stiffness is proposed according to analytical solution of averaged compressive stress-average deformation curve. Instability criterion of the pillar and roof strata system is proposed analytically (using) instability condition given by Salamon. It is found that the constitutive parameters of material of pillar, the geometrical size of pillar and the number of shear bands influence the stability of the system; stress gradient controls the starting time of slabbing, however it has no influence on the post-peak stiffness of the pillar.

Instability criterion for the system composed of elastic beam and strain-softening pillar based on gradient-dependent plasticity

A mechanical model is proposed for the system of elastic beam and strain-softening pillar where strain localization is initiated at peak shear stress. To obtain the plastic deformation of the pillar due to the shear slips of multiple shear bands, the pillar is divided into several narrow slices where compressive deformation is treated as uniformity. In the light of the compatibility condition of deformation, the total compressive displacement of the pillar is equal to the displacement of the beam in the middle span. An instability criterion is derived analytically based on the energy principle using a known size of localization band according to gradient dependent plasticity. The main advantage of the present model is that the effects of the constitutive parameters of rock and the geometrical size of structure are reflected in the criterion. The condition that the derivative of distributed load with respect to the deflection of the beam in the middle span is less than zero is not only equivalent to, but also even more concise in form than the instability criterion. To study the influences of constitutive parameters and geometrical size on stability, some examples are presented.

Elimination mechanism of coal and gas outburst based on geo‑dynamic system with stress–damage–seepage interactions

Coal and gas outburst is a complex dynamic disaster during coal underground mining.Revealing the disaster mechanism is of great signifcance for accurate prediction and prevention of coal and gas outburst.The geo-dynamic system of coal and gas outburst is proposed.The framework of geo-dynamic system is composed of gassy coal mass,geological dynamic environment and mining disturbance.Equations of stress–damage–seepage interaction for gassy coal mass is constructed to resolve the outburst elimination process by gas extraction with boreholes through layer in foor roadway.The results show the occurrence of outburst is divided into the evolution process of gestation,formation,development and termination of geo-dynamic system.The scale range of outburst occurrence is determined,which provides a spatial basis for the prevention and control of outburst.The formation criterion and instability criterion of coal and gas outburst are established.The formation criterion F1 is defned as the scale of the geo-dynamic system,and the instability criterion F2 is defned as the scale of the outburst geo-body.According to the geo-dynamic system,the elimination mechanism of coal and gas outburst—‘unloading+depressurization’is established,and the gas extraction by boreholes through layer in foor roadway for outburst elimination is given.For the research case,when the gas extraction is 120 days,the gas pressure of the coal seam is reduced to below 0.4 MPa,and the outburst danger is eliminated efectively.

Damage failure of cemented backfill and its reasonable match with rock mass

In order to study the failure mechanism of backfill and the reasonable matches between backfill and rock mass, and to achieve the object of safe and efficient mining in metal mine, four types of backfills were tested under uniaxial compression loading, with cement?tailing ratios of 0.250:1, 0.125:1, 0.100:1 and 0.083:1, respectively. With the help of the stress?strain curves, the deformation and failure characteristics of different backfills with differing cement?tailing ratios were analyzed. Based on the experimental results, the damage constitutive equations of cemented backfills with four cement?tailing ratios were proposed on the basis of damage mechanics. Moreover, comparative analysis of constitutive model and experimental results were made to verify the reliability of the damage model. In addition, an energy model using catastrophe theory to obtain the instability criteria of system was established to study the interaction between backfill and rock mass, and then the system instability criterion was deduced. The results show that there are different damage characteristics for different backfills, backfills with lower cement?tailing ratio tend to have a lower damage value when stress reaches peak value, and damage more rapidly and more obviously in failure process after peak value of stress; the stiffness and elastic modulus of rock mass with lower strength are more likely to lead to system instability. The results of this work provide a scientific basis for the rational strength design of backfill mine.

Flow instability criteria in processing map of superalloy GH79

Hot compression tests were conducted on a Gleeble-1500D thermal simulating tester.Based on the deformation behavior and microstructural evolution of superalloy GH79,different types of instability criteria of PRASAD,GEGEL,MALAS,MURTY and SEMIATIN were compared,and the physical significance of parameters was analyzed.Meanwhile,the processing maps with different instability criteria were obtained.It is shown that instability did not occur when average power dissipation rate was larger than 60%in the temperature range of 900-930°C and 960-1080°C,corresponding to the strain rate range of 5×10 -4 -1.8×10 -1 s -1 and 5×10 -4 -1.5×10 -1 s -1 ,respectively.The two domains are appropriate for the processing deformation of superalloy GH79.

Mechanical behaviors analysis of all position MAG weld pool instability

All position MAG welding is widely applied in pipeline processing. Whereas, welding defects easily happen when welding current is beyond 200 A. In this paper, the force equilibrium condition and influence mechanism of weld pool instability were discussed. Using the hysteresis tension theory on liquid interface, the radial and tangential force imposing on weld pool was analyzed to obtain the mechanical instability criterion on weld pool formation. The criterion provides a good explanation for those corresponding measures promoting weld pool formation in practice.

Web pillar stability in open‑pit highwall mining

When highwall mining technology is applied to recover large amounts of residual coal left under the highwall of a big openpit mine,a reasonable coal pillar width is required to ensure the stability of the web pillars.Using numerical simulations,this paper studied the characteristics of the abutment stress distribution in the web pillars under different slope angles and mining depths,and established a relation describing the stress distribution in the web pillar.The relationship between the abutment stress and the ultimate strength of the web pillar under different pillar widths was also analyzed.In combination with the failure characteristics of the pillar yield zone,this relationship was used to explore the instability mechanism of web pillars.Finally,the optimal retaining widths of the web pillars were determined.Based on the modeling results,a mechanical bearing model of the web pillar was established and a cusp catastrophe model of pillar-overburden was constructed.Additionally,the web pillar instability criterion was derived.By analyzing the ultimate strength of the web pillars,a formula for calculating the yield zone width either side of the pillars was established.Using the instability criterion of web pillars in highwall mining,a reasonable pillar width can be deduced theoretically,providing significant guidance on the application of highwall mining technology.

On theoretical research for nonlinear tearing mode

The analytical approaches for nonlinear tearing mode have been reviewed.It is shown that Rutherford＇s model has triggered numerous studies on the nonlinear tearing mode.Its physical picture is clear meanwhile its mathematical method is ingenious but still puzzling to understand.It is trying to find how the ＇nonlinear behavior＇ resulted from the linear equation by a nonlinear transform.It is indicated that Li＇s model for the tearing mode includes the linear growth,Rutherford＇s behavior and the new behavior.It was found that the quasilinear modification of magnetic field provided a new damping mechanism for nonlinear growth.The new behavior w~ t1/2 becomes dominant if the mode is weakly unstable.It is shown that many analytical methods have been developed to calculate the criterion parameter D＇ of the tearing mode.Li＇s instability criterion can cover the previous results in the limit cases.

On a plastic instability criterion for ultra-large radial-axial ring rolling process with four guide rolls

A dynamic mechanical model is proposed to describe the complexing actions of all the rolls on the ring during the ultra-large radial-axial ring rolling(RARR)process with four guide rolls.Based on the model,the calculation models for bending moment and normal stress at any section of the ring are deduced by force method.If the maximum section bending normal stress exceeds the yield stress of the ring materials,the ring will be distorted thus leading to the instability of the RARR process.According to this,a plastic instability criterion for the ultra-large RARR process with four guide rolls is developed,based on which a mathematical model to calculate the critical guide force for avoiding plastic instability of ring is obtained.The influence rule of the position of guide roll on the dangerous ring section of plastic instability is revealed,from which it is found the dangerous ring section mainly appears at the radial and axial deformation regions and the contact positions of the guide rolls and ring.The optimized layout of guide roll around the ring in favor of stability is determined to be about a1=61°and a2=119°.The plastic instability criterion is proven to be reliable from the aspects of the critical guide force,the section bending moment and normal stress and the dangerous ring section of plastic instability.Intelligent simulation case studies for the RARR process of ultra-large aluminum alloy ring indicate that the stable forming of the process can be effectively realized by regulating the guide force based on the plastic instability criterion.This work could provide a valuable guidance for the control of guide rolls and the optimization of the ultra-large RARR process with four guide rolls.

A Comparative Study of Various Flow Instability Criteria in Processing Map of Superalloy GH4742

Hot compression tests were conducted on a Gleeble-1500D thermal simulating tester. Based on the deformation behavior and microstructural evolution of superalloy GH4742, different types of instability criteria of Prasad, Gegel, Malas, Murty and Semiatin were compared, and the physical significance of parameters was analyzed. Meanwhile, the processing maps with different instability criteria were obtained. It was shown that instability did not occur when average power dissipation rate was larger than 50% in the temperature range of 1020- 1130℃, corresponding to the strain rate range of 5 × 10-4-3.2 × 10-3 s-1. The domain is appropriate for the processing deformation of superalloy GH4742.

Study on the onset temperature of a standing-wave thermoacoustic engine based on circuit network theory

Onset mechanism is one of the most fundamental issues in thermoacoustic field.However,the onset conditions and the phenomena happening in the onset process have not been well explained theoretically.In this paper,a novel model based on the circuit network analogy is proposed to predict the onset temperature of a standing-wave thermoacoustic engine.The activity and instability criteria are proposed to be the onset criteria in the model.The influences of the porosity of the heat exchanger and the stack,and the length of the resonant tube on the onset temperature are analyzed.The calculated results are in agreement with the experimental results,which indicates that the activity and instability criteria can be used to predict the onset conditions of a thermoacoustic engine.