Abstract The **failure** **criterion** is an essential part of all strength calculations of design. It was shown in the past that the tensor-polynomial equation could be regarded as a polynomial expansion of the real **failure** surface. Now it is shown that the third-degree polynomial is identical to the real **failure** **criterion**. It is also shown that the second-degree part of the polynomial is identical to the orthotropic exten- sion of the von Mises **criterion** for initial yield. The third- degree polynomial hardening terms of the **criterion** are also shown to incorporate the earlier theoretical explained mixed-mode I-II fracture equation, showing hardening to be based on hindered microcrack extension. For uniaxial loading, the **failure** **criterion** can be resolved in factors, leading to the derivation of extended Hankinson equations. This allows the relations between the constants of the total **failure** **criterion** to be elucidated, which is necessary for data fi tting of this **criterion** and providing a simple method to determine the constants by the simple uniaxial, oblique- grain compression and tension tests. Based on this, the numerical **failure** **criterion** is given with the simple lower bound **criterion** for practice and for the codes.

3.1 Example 1: Grain Size Effects in Copper Work by Escobedo et. al investigated four di ff erent grain size ranging from 30-200 µm in copper to study the e ff ect of grain size on the spall strength and total nucleated dam- age within the samples [17]. The results from this study showed that the measured spall strength was independent of grain size. In fact, the PDV profiles were found to be identical for each study except for the slope of the pull- back signals. If spall strength is simply the stress required to nucleate a void within a sample and the distribution of the weak links in form of grain boundaries in the different samples was unchanged then these results would be valid. However, postmortem analysis of these materials showed that the total damage in the recovered sample varied as a function of grain size, which is inconsistent with the con- clusions solely derived from the PDV profiles. This work highlights the importance of sample recovery in experi- ments focusing on understanding the role of microstruc- ture on damage and **failure**. The new **failure** **criterion** ap- plied to the data reported in the paper to test the robustness

Abstract. From theory to experience, earthquake probability associated with an active fault should be gradually increas- ing with time since the last event. In this paper, a new non- stationary earthquake assessment motivated/derived from the Mohr–Coulomb **failure** **criterion** is introduced. Differ- ent from other non-stationary earthquake analyses, the new model can more clearly define and calculate the stress states between two characteristic earthquakes. In addition to the model development and the algorithms, this paper also presents an example calculation to help explain and validate the new model. On the condition of best-estimate model pa- rameters, the example calculation shows a 7.6 % probability for the Meishan fault in central Taiwan to induce a major earthquake in years 2015–2025, and if the earthquake does not occur by 2025, the earthquake probability will increase to 8 % in 2025–2035, which validates the new model that can calculate non-stationary earthquake probability as it should vary with time.

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To anticipate **failure** in a warming climate, we need to im- prove the understanding of how rock–ice mechanical compo- nents control rock slope destabilisation and **failure** between − 10 and 0 ◦ C. Generally, warming of permafrost in rock slopes affects the shear stress along sliding planes in terms of (i) fracture toughness of rock bridges, (ii) friction of rock- rock contacts, (iii) ductile creep behaviour of ice and (iv) brit- tle **failure** of ice infillings (Krautblatter et al., 2013). Whereas the mechanics of frozen rock (Glamheden and Lindblom, 2002; Kodama et al., 2013; Mellor, 1973), the mechanics of frozen rock joints without fillings (Dwivedi et al., 2000; Krautblatter et al., 2013), and the ductile temperature- and stress-dependent creep of ice and ice-rich soils (Arenson and Springman, 2005a; Sanderson, 1988; Yamamoto and Spring- man, 2014) have been investigated in a number of studies, the brittle **failure** of ice infillings is still poorly understood. We hypothesise that the brittle **failure** of ice infillings (i.e. either along rock–ice interfaces or inside the ice) is a common final **failure** mechanism, which is documented by numerous ex- posed ice-filled joint surfaces subsequent to **failure**. It is me- chanically dependent on fast deformations (i.e. strain rates) and thus is likely to control the final **failure** of many recent events. This study aims at developing the first comprehensive temperature- and stress-dependent brittle **failure** **criterion** for ice-filled joints based on shear tests on rock–ice–rock sam- ples.

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Reliable line production processes and simulation tools play a central role for the structural inte- gration of thermoplastic composites in advanced lightweight constructions. Provided that materi- al-adapted joining technologies are available, they can be applied in heavy-duty multi-material designs (MMD). A load-adapted approach was implemented into the new fully automatic and fault- tolerant thermo mechanical flow drill joining (FDJ) concept. With this method it is possible to manufacture reproducible high strength FRP/metal-joints within short cycle times and without use of extra joining elements for the first time. The analysis of FDJ joints requires a simplified mo- del of the joint to enable efficient numerical simulations. The present work introduces a strategy in modeling a finite-element based analogous-approach for FDJ-joints with glass fiber reinforced polypropylene and high-strength steel. Combined with a newly developed section-force related **failure** **criterion**, it is possible to predict the fundamental **failure** behavior in multi-axial stress states. The functionality of the holistic approach is illustrated by a demonstrator that represents a part of a car body-in-white structure. The comparison of simulated and experimentally deter- mined **failure** loads proves the applicability for several combined load cases.

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In many of these studies, the ability of strength-based and energy-based criteria to accurately predict material **failure** was compared. Martin [36] considered both a strength-based **failure** **criterion**, utilizing the Tsai Hill **criterion**, and an energy- based **failure** **criterion**. While the energy-based **criterion** was found to accurately predict the onset of **failure**, the strength-based method did not. The author noted that the weakness in the strength-based approach is due to the lack of adequate test methods being available to determine the material through thickness strength, and the inability to evaluate the stresses at the crack tip due to the presence of a singularity. The author strongly recommended the use of energy- based **criterion** to predict crack propagation in composite materials. Following NASA’s lead, others investigated delamination through a similar approach. It was concluded that energy-based methods provided a more reliable and accurate method than strength-based methods for predicting the initiation and growth of interlaminar delamination cracks [37].

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The testing program usually depends upon the aim of the investigation. If only the shear strength parameters of a certain soil are of interest, disturbed specimens are tested. In this case some few tests are carried out on normally consolidated specimens (theoretically, one test is sufficient if the consolidation behavior of the soil is known, otherwise two tests are needed) and a few tests on over-consolidated specimens (theoretically one is suf- ficient). The over-consolidation ratio is defined as the ratio of the maximum normal load to the load under which the specimen is sheared. From the results of these tests the shear **criterion** can be established (refer to [11] [15]). Where undisturbed specimens are tested, the over-consolidation ratio of every specimen can be established if, at best, one shear test is carried out on remoulded and normally consolidated specimens of the same soil type. The diagrams in Figure 15 should explain the relationships between the parameters.

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The maximum surface pressure loaded on the post on the mechanical experiment was consistent with the value on FEA, with a maximum error of 14.4%. Accordingly, the results of FEA may have been valid. On FEA, not only the surface pressure but also the Von Mises-equivalent stress and shear strain can be determined, and these cannot actually be measured. If the results of FEA are valid, these values may be reliable. Von Mises-equivalent stress is used as a yield index of materials for strength-designing, and it was considered appropriate to be used as a **criterion** of post breakage, which is the objective of this study.

concerned. For this reason, the aim of this paper is neither to promote the use of the **criterion** in engineering nor to undermine it, but to develop the **criterion** as a theory to its full maturity for UD composites such that those who favour the theory will have a better reason to continue their practices with likely improved level confidence while those objecting it will have the full facts in front of them to support their views. Equally true, having the full facts established, some of the users might change their views either way. It is not for this paper to dictate the readers’ views and users still have to come to their own assessments objectively and intellectually. For this reason, no efforts will be made to compare with experimental results to justify or disapprove the **criterion**. Ultimately, experimental data will serve as the proof but such data are unavailable. There is therefore a desperate need for them to be made available in order to address the **failure** of composites.

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2. They will be cost and time saving, because they are not based on the curve fitting of the experimental data for each specific system of composite. As an example, when the value of fibre volume fraction in a specific composite material changes, a new series of mechanical testing is required to characterize fracture properties of the new system. 3. They can be used in the design of the composite system by selecting different types of the constituents or by changing the constituent property or their portion in the composite. In this research, a mechanistic mixed mode **criterion** based on the fully understanding of the **failure** mechanisms involved in the through thickness fracture of UD polymer composite will be developed. To develop a mechanistic model, the major **failure** mechanisms occurring during fracture and their corresponding energy absorbing mechanism and the amount of energy released will be understood and determined. The fractography will be done by the help of scanning electron and optical microscopy images. The major **failure** mechanisms for the through thickness of UD composite will be resin fracture, and fibre/matrix debonding that will be studied carefully. To derive equations for the values of energy released by the fracture of UD composite, anisotropy of UD composite will be considered and the relations will use LEFM.

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circumferential directions, respectively; Nxφ is the shear stress resultant which is zero due to the symmetry of the lamination. The first-ply **failure** analysis of the laminated composite pressure vessel is performed via the use of a suitable **failure** **criterion**. Herein, a number of phenomenological **failure** criteria are adopted in the analysis. For comparison purpose, the laminated composite pressure vessel is also analyzed using the finite element method which is formulated on the basis of the first-order shear deformation theory [11].

Abstract: - Investigation was carried out on the slope stability of lateritic soil due to effects of some geotechnical properties in selected burrow pits in Akure, Ibadan, Ewekoro and Iperu areas, south western, Nigeria. The geotechnical properties were determined in accordance with American Society for Testing and Materials (ASTM) Standards. The conventional slope stability analysis was based on the linear Mohr – Coulomb **failure** **criterion** utilizing the notion of safety factors with respect to shear strength, where their average results of cohesion, angle of friction, bulk density and moisture content from the locations are 82 kPa, 18 degree, 1700 kg/m 3 , and 22 % respectively. The average specific gravity for locations was 2.73. The degree of permeability was very low except for location 6 in Ibadan area which is medium. The grain size distribution for the locations was classified into SC – SM (silt clayey sand). From compaction test, average moisture content, average wet density and dry density for the locations are 23 %, 1849 kg/m 3 and 1512 kg/m 3 respectively while the average compaction curve deduced 24 % optimum moisture contents and 1639 kg/m 3 maximum dry density. The Atterberg limits test results indicate that locations 1 – 5 were recorded as plastic soil while location 6 non- plastic soil. Also, the linear shrinkage degree of expansion for location 1 – 5 indicates critical while location 6 indicates non-critical. Finally, statistical mathematical model equations were developed. The factor of safety for locations 1 – 5 was satisfactory for routine extraction and loading operations while location 6 was unsafe due to loading conditions of the terrain.

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**Failure** **criterion** is a parameter to represent the resistance to **failure** of locally wall thinned pipe, and it depends on material characteristics, defect geometry, applied loading type, and **failure** mode. Therefore, accurate prediction of integrity of wall thinned pipe requires a **failure** **criterion** adequately reflected the characteristics of defect shape and loading in piping system. In the present study, the finite element analysis was performed and the results were compared with those of pipe experiment to develop a sound **criterion** for **failure** of internally wall thinned pipe subjected to combined pressure and bending moment. By comparing the predictions of **failure** with actual **failure** load and displacement, an appropriate **criterion** was investigated. From this investigation, it is concluded that true ultimate stress **criterion** is the most accurate to predict **failure** of wall thinned pipe under combined loads, but it is not conservative under some conditions. Engineering ultimate stress estimates the **failure** load and displacement reasonably for all conditions, although the predictions are less accurate compared with the results predicted by true ultimate stress **criterion**.

In the framework of a CEA research programme, conducted in partnership with IRSN, EDF and INSA Lyon, Compact Tension (CT) specimens have been tested to characterize the tear resistance of various French RPV 16MND5 steels at very high temperatures ranging from 900°C to 1100°C. The aim of this experimental program was to contribute to the definition of a tearing **criterion** by identifying the related material parameters at temperatures representative of the real severe accident conditions. The influence of metallurgic composition on the kinetics of tearing was taken into account as a previous work on different RPV steels has shown a possible loss of ductility at high temperature depending on the initial chemical composition of the vessel material. A **failure** **criterion**, noted G fr ,

Element rotation has been ignored by previous RFEM-based limit analyses by other researchers and the main purpose was to maintain the condition of no gap or overlap between neighboring elements. Although it appears to be reasonable for the translation-dominant type of slope **failure**, the assumption proves to be inadequate to describe cases (such as upwelling underground water or increase in the height of soil slopes) where the rotation may be a contributing factor. The **criterion** is generalized based on the toppling **failure** **criterion** originally proposed by Goodman and Bray (1981). Consider a block on an inclined surface subjected to self-weight only (Fig. 3). Fig. 3 shows a state in which a rotation or toppling of the block is pending. The critical condition can be expressed as:

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analysis. The Tsai-Hill **criterion** was used to assess the **failure** of composite pressure vessel. The stress distribution and Tsai-Hill **failure** **criterion** are dis- cussed for the inner two layers of composite pressure vessel at the junction of semispherical part. It can be concluded that layer 2 **failure** occurred for the composite pressure vessel studied under first type boundary condition; while layer 1 failed for the composite pressure vessel under second type boundary condition.

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0.59, slope equal to 0.56 and intercept equal to 1475N in Naylor's study). This improvement is probably due to the better match between the computational and experimental boundary conditions as well as the new optimization of the **failure** **criterion**. In particular, the proximal femora were loaded in the plane containing both proximal and femoral neck axis, which was also similar to the plane perpendicular to the DXA scanning. Therefore, the out of axis loads, not reproducible in a 2D model, were minimized in this case. The DXA-based FE models for the SIDE con ﬁ guration were found to provide similar coef ﬁ cient of determination when com- pared to the results reported by Den Buijs and Dragomir- Daescu (2011), who used projected images from QCT scans to estimate the bone stiffness in a simulated fall. While this result may suggest similarities between the predictive ability of models generated from real DXA images or from projected QCT scans, the differences between the models, the studied sample size, and the comparison between predicted and measure mechanical properties recommend further analyses to be done.

of the dopant cations in the vicinity of the grain boundaries. The co-doping of Ti and Ge cations increases the grain size at the time of **failure**, which can be regarded as a parameter to give a limit of stress for high temperature **failure**. The parameter of the critical grain size at the time of **failure** correlates well with the value of overlap population in cation- doped TZP model cluster obtained from a ﬁrst-principle molecular orbital calculation. The covalent bond at the grain boundaries plays a critical role in the high temperature tensile ductility of TZP.

The objective of this study is to evaluate the potential of light alloy mechanical part use in automobile industry by studying their fatigue life using various parameters such as effect of suspension dynamic, excitation type, geometry and mechanical part weight. The studied part is the lower suspension arm made from 7075-T6 aluminium alloy. The strain density energy approach enables us to compare two same order tensor: the multiaxial and uniaxial cases. The random displacement excitation is obtained analytically from the power spectral density PSD. The force excitation is obtained by a simple normalisation of spectrum displacement. To avoid the use of Newton-Raphson method during the partial fatigue life calculation step in all mesh elements, a Matlab interface to identify the critical elements is developed. The strain energy density (SENER) signal of the critical element is corrected to remove anomalies by WAFO Matlab interface algorithm. Rainflow cycles are extracted using Markov formulation in order to calculate the number of signal repetitions to **failure**, which is calculated from Miner law.

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Vibration **failure** of piping is a serious problem and a matter of concern for safety and reliability of plant operations. Fatigue is the main cause of such failures. Due to the complexity of the phenomenon no closed form design solutions are available. In our study an analytical technique based on the theory of vibrations in the time domain has been pre- sented. Using the inverse theory, the problem has been reduced to a system of Volterra Integral equations to be solved simultaneously at every time step. The solution of the inverse problem may be used in the conventional method to cal- culate stresses and end reactions which are important from the perspective of engineering design and condition moni- toring. The method is robust, simple and can be easily adopted by practicing engineers.