Mohr Failure Criterion Research Articles

A failure envelope proposal based on the analysis of the requirements of nonlinear Mohr-Coulomb criteria

Nonlinear Mohr failure criterion is re-evaluated in this paper. It has been revealed that the polynomial failure criteria constructed by the normal stress σn and the shear stress τn predict the fracture angles unreasonably, and their predictions are also inconsistent with experimental observation that the two branches of failure envelope trend to be parallel to σn axis under high hydrostatic compression. In order to overcome the problems, first, the transformation of failure functions from the principal stress space (σ1, σ3) to the stress space (σn, τn) is derived. Then the failure function is expressed in terms of the principal stresses, and it is converted from the principal stress space (σ1, σ3) to the stress space (σn, τn) based on the transformation. The present failure criterion predicts more reasonable failure angles, and its envelope trends to be parallel to σn axis under high hydrostatic compression. In particular, the paper reveals that for brittle materials the fracture angle under the uniaxial tension is not 0° although the fracture surface is nearly perpendicular to the direction of the loading; under the pure shear stress the angle between the fracture surface and the direction of the loading is not 45° although it is close to 45°. The present criterion predicts this physical phenomenon reasonably.

An Experimental and Numerical Study of Damage Due to Particle Impact on Sapphire Orifices Used in High-Pressure Water Jet Cutting

In the present study, the damage mechanisms that cause premature failure of sapphire water jet orifices were analyzed using a combined experimental and finite element modeling (FEM) approach. Depending on the operating behavior and local conditions, the service life of orifices for high-pressure water jet cutting often deviates considerably from the manufacturer’s specifications. Literature states a typical service life of 50 to 100 h, while in some cases, premature failure after a few hours or even minutes of operation can be observed. The focus of this paper is on the interaction of particles that impact the orifice surface but also the effect of faulty orifice assembly is taken into account. To estimate the risk of failure, the stress distribution in critical parts of the orifice were calculated via FEM, which is fed with experimental data. The modified Mohr failure criterion was then used to evaluate the stress distributions with respect to the possible failure of the orifice jewel. The results revealed that the risk of damage caused by excessive assembly preload forces is marginal. The stress caused by the impact of particles of different sizes is up to four orders of magnitude higher than the stress caused by assembly forces and is therefore identified as the main risk for orifices to fail prematurely. Experimental data shows mainly particles of calcium carbonate and iron–aluminum silicates, which are compounds that originate from the process water itself. It is demonstrated that particles are more critical than formerly assumed in the literature. This paper identifies particles with a diameter of more than 10 µm as critical when there are no other loads present. In operation, even particles as small as 2 µm in diameter can cause damage to the orifice jewel. To prevent premature orifice failure due to foreign particles, water filtration with a 2 µm mesh is recommended, while future research needs to focus on the interior cutting head design to prevent precipitation from the process water.

Study on failure mechanism of line contact structures of nuclear graphite

Line contact structures, such as the contact between graphite brick and graphite tenon, widely exist in high-temperature gas-cooled reactors. Due to the stress concentration effect, the line contact area is one of the dangerous positions prone to failure in the nuclear reactor core. In this paper, the failure mechanism of line contact structures composed of IG11 nuclear graphite column and brick were investigated by means of experiment and finite element simulation. It was found that the failure process mainly includes three stages: firstly, the damage accumulation in nuclear graphite material led to the characteristic yielding of the line contact structure, but no macroscopic failure can be observed at this stage; secondly, the stresses near the contact area met Mohr failure criterion, and a crack initiated and propagated laterally in the contact zone, that is, local macroscopic failure occurred at this stage; finally, a second crack initiated in the contact area and developed in to a Y-shape, resulting in the final failure of the structure. This study lays a foundation for the structural design and safety assessment of high-temperature gas-cooled reactors.

Ultimate state criteria and strength characteristics of the rock massifs being undermined repeatedly

Methodological approaches to the selection of ultimate state criteria and strength characteristics of the repeatedly undermined rock massifs were developed. These approaches were designed to provide parametric support to the geomechanical modelling of the massif stress-strain state and the mining systems of the Starobin potash deposit mine fields planned for the additional mining of the mineral reserves left. It was established that a complex criterion must be used to study the massif ultimate state. Determination of such criterion can be carried out using the developed approaches. The first approach is to select several criteria that evaluate the massif ultimate state by certain types of the massif stress-strain state. These criteria are the following: the criterion of the maximum normal stresses, criterion of the maximum linear strains, the criterion of the maximum shear stresses and the Coulomb–Mohr failure criterion. The second approach is to construct an integrated failure state criterion for materials whose ultimate tensile and compressive stresses differ significantly. In this case, parameters characterizing the type of stress state and properties of the material are introduced. These parameters together determine the destruction character – tear or shear. To describe the rocks behavior in the extreme strength stage of deformation, it is proposed to apply deformation theory of strength using the developed strain failure criterion. When calculating the strength characteristics of the repeatedly undermined rock massif, it is recommended to use a structural attenuation coefficient as the product of several factors, taking into account various types of disturbances in the primary undermined massif and the time factor. The Coulomb–Mohr strength condition is recommended to be used taking into account the composite structural attenuation coefficient. Dependencies have been developed to describe the change in the strength characteristics of rocks in the undermined massif, considering the attenuation coefficient.

Influence of "MOTRCS" factors on the performance of various direct and indirect restorations: A finite element analysis.

Aim of the Study:The purpose of the study is to evaluate the occlusal relationship of the mesiobuccal cusp of a mandibular first molar with the marginal ridge of maxillary first molar and second premolar and to analyze the effect of the above occlusal relation on different direct and indirect restorations using finite element analysis (FEA).Methodology:Four hundred volunteers studying in a dental college were screened, of which 100 volunteers were selected for studying occlusal relationships based on the inclusion and exclusion criteria. The two most common occlusal relationships were considered for analyzing two direct (amalgam and direct composite restorations) and two indirect restorations (composite and ceramic restorations). Three-dimensional (3D) scanning of the models was performed, and Class II tooth preparations specific for each restorative material were prepared digitally on 3D models. FEA was employed to study von Mises (VM) stress, principal stresses, and cuspal deflection for each restorative material, and failure of the tooth-restoration unit was calculated using the modified Mohr failure criterion.Results:Among all the analyzed materials, cuspal deformation, principal stresses, and VM stresses were high for direct composite restoration and least for ceramic inlay. According to modified Mohr criteria, except for direct composite, all other materials performed better.Conclusion:Silver amalgam and ceramic restorations presented with minimal stress concentration and cuspal deflection, and Type I occlusal relationship presented with higher stress concentration compared to Type II.

A reflection on the Mohr failure criterion

The Mohr failure criterion has been re-examined and re-presented in a rational manner in the context of brittle materials. The generic assumptions and their logical inferences have been elaborated, as well as the basic assumption of the isotropy of the material. It has been revealed for the first time that the assumption that ‘failure is determined by the stresses exposed on the fracture plane’ relies on the basic assumption of isotropy and its adoption in the establishment of popular modern failure criteria for anisotropic composites is therefore deemed to be out of context. Based on the generic assumptions and well-established experimental observations on the fracture of brittle materials under uniaxial tension, pure shear and uniaxial compression and through rational reasoning, the characteristics of the failure envelope on the tensile side have been deduced, revealing many features which have never been fully established previously. From the perspective of the Mohr criterion, the Coulomb-Mohr criterion has been given a thorough and objective appraisal, leading to a complete dismissal of it as a criterion of practical relevance.

Lower Bound Solution of Foundation Bearing Capacity beneath Strip Footing Based on Parabolic Mohr Failure Criterion

The static allowable stress field of foundation under strip foundation is constructed by means of stress columns, and the calculation method of the lower bound foundation bearing capacity based on the two‐parameter parabolic Mohr yield criterion is proposed. Moreover, the influence of the amount of stress columns and material mechanical parameters on the lower bound bearing capacity is analyzed. The results show that a better solution can be obtained by optimizing the static allowable stress field. However, the improvement of lower bound solution might be inefficient if the stress column amount is large enough. The stresses of the superimposition area show a reduction with the improvement of stress field; on the other hand, the superposed stresses are enhanced ever faster as the involved stress column increases. The tensile‐compressive strength ratio has a moderate effect on the lower bound solution. Finally, the reliability of the proposed method is verified by some rock foundation loading tests.

Excavation damaged zone depths prediction for TBM-excavated roadways in deep collieries

The excavation works at underground mines create excavation damage zone (EDZ) in surrounding rocks around roadway geometry. The EDZ depth is a critical parameter for stability analysis, risk assessment support design and toxic waste leakage. This paper proposed an innovative EDZ depth prediction based on a modified nonlinear Mohr failure criterion and modification of conventional analytical solution by means of perturbation method. A set of cyclic loading tests of surrounding rock of roadways are conducted, and a modified Mohr failure criterion of rocks under cyclic loading path of TBM excavation is established on the basis of test results. Moreover, perturbation method was introduced for enhancing calculation accuracy. In order to verify the proposed analytical solution, a set of in situ digital panoramic borehole camera image monitoring was carried out within the roadways and the monitoring results correlated well with the proposed analytical solution. The EDZ geometries of roadways in deep mines are typically oval, and the EDZ depth is influenced by ground stress magnitude, lateral coefficient and support stress significantly. Through the proposed analytical solution, a more accurate prediction of EDZ depth of roadways can be obtained conveniently before the excavation works.

A finite strain solution for the elastoplastic ground response curve in tunnelling: rocks with non‐linear failure envelopes

SummaryThis paper generalizes the finite strain Coulomb solution of Vrakas and Anagnostou (Int J Numer Anal Meth Geomech 2014; 38(11): 1131–1148) for the classic tunnel mechanics problem of the ground response curve to elastoplastic grounds satisfying a non‐linear Mohr's failure criterion. A linear (Coulomb‐type) plastic potential function is used, leading to a non‐associated flow law, and edge plastic flow is considered in the plastic zone. The solution for a general non‐linear Mohr's failure criterion is semi‐analytical in that it requires the evaluation of definite integrals. In the special case of the Hoek–Brown criterion, however, these integrals are calculated analytically, resulting in a rigorous closed‐form series solution. The applicability of the derived solution is illustrated through the example of the Yacambú‐Quibor tunnel, where very large deformations were observed when crossing of weak graphitic phyllites. Copyright © 2016 John Wiley & Sons, Ltd.

Determination of the Breaking Load for Concrete Slabs Based on the Deformation Theory of Plasticity

The paper proposes a technique of determining the maximum critical load for concrete slabs based on the deformation theory of plasticity by G.A. Geniev. To solve the problem the method of successive loading is used. Physically nonlinear problem is reduced to successive solution of elastic problems for the construction with a variable elasticity modulus and Poisson's ratio within height. In deriving equations, we take in account cracking in the tension zone of concrete, creep of concrete and nonlinear behavior of steel reinforcement. The work of steel is described by the Prandtl diagram. For the tensile zone, we use Mohr's failure criterion. We perform the solution numerically using the finite difference method. The problem reduces to the fourth-order differential equation for the deflection. We compare our results with the experimental data for square plate, hinged on the contour and uniformly loaded.

Mechanical genesis of Henan (China) Yima thrust nappe structure

Considering the serious coal and rock dynamic disasters around the main slip plane called F16 in the coal mining area) of Henan Yima (China) thrust nappe structure, the mechanical genesis of the Yima thrust nappe structure was studied comprehensively using geomechanics, fault mechanics, elastic mechanics, and Coulomb’s law of friction. First, using the centrifugal inertia force of Earth’s rotation as a source, a mechanical model of N-S compression superimposed with W-E reverse torsion was established to explain the formation of the early Yima coal basin and Jurassic Yima Group coal measures. Second, an equation for the ultimate stress in the forming stage of F16 was derived using the plastic slip-line field theory and the parabolic Mohr failure criterion. Moreover, the distribution of ultimate stress and the geometric characteristics of the fault profile were obtained using the field model parameters. Finally, the stress field of F16 and the mechanical genesis of the large-scale reverse thrust sheet were discussed based on elastic mechanics theory and Coulomb’s law of friction. The results show that the tectonic framework of the early Yima coal basin and the formation pattern of Jurassic Yima Group coal measures given by the model are consistent with the in-situ explorations. The geometric characteristics of the fault profile obtained by numerical calculation can better reflect the shape of F16 in its forming stage, and the mechanical genesis of the large-scale reverse thrust sheet also concurred with the field situations. Thus, this work can provide a foundation for further studies on the genesis of the thrust nappe structure, the mechanism of rock bursts induced by F16, and the characteristics of the residual stress field in the Yima mining area.

Model of Equal-Stressed Cylinder Based on the Mohr Failure Criterion

In this article, an analytical dependence of distribution of elasticity modulus across the thickness of the cylinder loaded with internal pressure p, at which the equivalent stresses according the Mohr failure criterion are the same at all points. The problem is solved for the cases of plane strain state and plane stress state in the elastic formulation.

The Bearing Capacity of Circular Footings in Sand: Comparison between Model Tests and Numerical Simulations Based on a Nonlinear Mohr Failure Envelope

This paper presents the results of a series of triaxial tests with dry sand at confining pressures varying from 1.5 kPa to 100 kPa at relative densities of 0.20, 0.59, and 0.84. The results, which are in reasonable accordance with an equation given by Bolton, show that the friction angle is strongly dependent on the stress level and on the basis of the test results, a nonlinear Mohr failure criterion has been proposed. This yield criterion has been implemented in a finite element program and an analysis of the bearing capacity of a circular shaped model foundation, diameter 100 mm, has been conducted. Comparisons have been made with results from 1g model scale tests with a foundation of similar size and a good agreement between numerical results and test results has been found.

Microstructural evidence of low‐strain, time‐transgressive subglacial deformation

AbstractMicrostructural analyses were used to investigate the formation of a macroscale‐massive till at Knud Strand in Denmark. More than 100 thin sections were examined and microstructures mapped and counted for quantitative comparison and interpretation. Microstructures indicative of both brittle (grain lineations, edge‐to‐edge crushed grains) and ductile (turbate structures) deformation are evenly distributed in vertical profiles through the till, suggesting that strain contributed to its formation. Discrete shears (grain lineations and plasmic fabric) probably accommodated most deformation, whereas rotational deformation was less prominent. The microshear geometry fits the predicted Coulomb–Mohr failure criterion, indicating that till behaves as a plastic material. Strain estimate of ca. 101 from micromorphological proxies is two–three orders of magnitude lower than expected if the till was subjected to pervasive deformation. A hybrid of lodgement and time‐transgressive deformation is envisaged as the till‐forming processes. Our data suggest that even abundant evidence of microscale deformation at continuing high levels of strain may only record the latest process of deposition and deformation and therefore not fully reflect the complexity of till genesis. Copyright © 2007 John Wiley & Sons, Ltd.

Spiral point drill temperature and stress in high-throughput drilling of titanium

The spatial and temporal distributions of the temperature and stress of a 9.92 mm diameter spiral point drill are studied in high-throughput drilling of Ti–6Al–4V with 384 mm 3/s material removal rate (MRR). A finite element thermal model using the inverse heat transfer method is applied to find the heat partition on the tool–chip contact area and convection heat transfer coefficient of cutting fluid. The thermal model is validated by comparing experimentally measured and numerically predicted drill temperature with good agreement. Thermo-mechanical finite element analysis is applied to solve the drill stress distribution. Modeling results confirm that the supply of cutting fluid is important to reduce the temperature across the drill cutting and chisel edges. At 183 m/min peripheral cutting speed, 0.05 mm/rev feed and 10.2 mm depth of drilling, the drill peak temperature is reduced from 1210 °C in dry drilling to 651 °C with cutting fluid supplied through the drill body. Under the same MRR, 61 m/min peripheral cutting speed and 0.15 mm/rev feed, the analysis shows that the drill peak temperature is reduced to 472 °C. The temperature induced thermal stress combined with the mechanical stress caused by cutting forces is analyzed to predict the location of drill failure. Applying the modified Mohr failure criterion, the drill cutting and chisel edges are found to be prone to failure in dry and wet drilling conditions, respectively. This study demonstrates the effectiveness of drill thermal and stress modeling for drilling process parameter selection and drill design improvement.

Failure behavior of an epoxy matrix under different kinds of static loading

The yield and fracture behavior of an unreinforced epoxy resin has been investigated. The parabolic Mohr failure criterion was applied to experimental results under different loading conditions. From a plain resin slab, specimens for tensile, torsion and compression tests were manufactured and the failure behavior of the resin was tested and discussed in detail. The results of the mechanical tests and a fractographic study of the fracture surfaces were correlated with the stress-state-dependent strength and fracture stress of the epoxy resin. This plays an important role in fiber-reinforced composites because just after cooling to room temperature the resin matrix is under a tri-axial residual stress state. From the mechanical properties of the plain resin and by using the parabolic failure criterion it is possible to explain the low strain to failure of unidirectional laminates under transverse tensile loading.

Characterizing the Failure Envelope of a Conductive Adhesive

This paper focuses on mechanical testing designed to determine the static failure envelope for a conductive adhesive. Samples were made by bonding copper pegs together with the conductive adhesive. The samples were then tested at various loading conditions including tension, tension shear, and compression shear. Results were analyzed in order to check for correlations between the data and the testing procedures. The statistical distribution of the data was also analyzed. Furthermore, a finite element model of the test sample was constructed and used to verify the assumptions made with respect to the interpretation of the data. The data from various loading conditions was then used to construct the static failure envelope of the material. A modified Coulomb–Mohr failure criterion was used to model the failure envelope of the conductive adhesive. This criterion contains four material constants to be determined experimentally. Once these parameters are determined, a failure envelope can be easily constructed. The envelope can then be used to predict failure at any combination of shear and normal stresses. The test results showed that the empirical data are well characterized by the modified Coulomb–Mohr failure envelope.

Is internal friction friction?

Mogi [1974] proposed a simple model of the incipient rupture surface to explain the Coulomb failure criterion. We show here that this model can plausibly be extended to explain the Mohr failure criterion. In Mogi's model the incipient rupture surface immediately before fracture consists of areas across which material integrity is maintained (intact areas) and areas across which it is not (cracks). The strength of the incipient rupture surface is made up of the inherent strength of the intact areas plus the frictional resistance to sliding offered by the cracked areas. Although the coefficient of internal friction (slope of the strength versus normal stress curve) depends upon both the frictional and inherent strengths, the phenomenon of internal friction can be identified with the frictional part. The curvature of the Mohr failure envelope is interpreted as a consequence of differences in damage (cracking) accumulated in prefailure loading at different confining pressures.

A plasticity model for punching shear of laterally restrained slabs with compressive membrane action

A plastic theoretical model is presented for the punching shear failure of laterally restrained concrete slabs, in which a parabolic Mohr failure criterion for concrete is adopted. The proposed method allows for the effect of compressive membrane action and a membrane-modified flexural theory of elasto-plasticity is used to calculate the compressive membrane forces. The predictions by the proposed analysis show good agreement with a wide range of experimental test results.

Reliability Analysis of Mohr Failure Criterion

For biaxial states of stress in mass concrete structures, safety can be assessed in terms of the Mohr failure criterion. Safety is generally evaluated by a deterministic factor of safety. When loads vary and material properties are not known with certainty, reliability analysis evaluates safety probabilistically. In this paper, deterministic and probabilistic safety evaluations are compared in terms of levels of uncertainty associated with load and resistance parameters and the extent is indicated to which the probabilistic approach is more informative than the deterministic approach. The effect on this comparison of several characteristics of concrete material is investigated. Three widely recognized design criteria are likewise compared.