Combined Loading Conditions Research Articles

Analysis of the stress state in QFN package during four point bending and temperature experiments utilizing piezoresistive stress sensor

This article reports a comprehensive study on four point bending and temperature experiments and their correlation with numerical simulation. The test vehicle is a printed circuit board (PCB) with 16 Quad Flat No Leads Packages (QFNs) components mounted on top and bottom side. Each QFN has 120 stress sensing cells distributed over the surface of the silicon die. In our experiments we have investigated the stress state in the QFN utilizing these piezoresisitve stress sensors for thermal, four point bending and combined loading conditions. In our study we compare these measurements with the numerical model. Stress analysis for the isothermal bending case showed that components very close to the edge are exposed to slightly higher stresses (20 %) compared to the components placed in the center of the PCB.

Behavior of Mono Helical Pile Foundation in Clays under Combined Uplift and Lateral Loading Conditions

Offshore wind energy development is driven by ongoing research and development to determine technological issues connected with offshore wind turbines. A fundamental design difficulty is the offshore wind turbine foundations. By far, one of the most commonly practiced foundation systems is mono helical pile foundations because of their simplicity and resilience. Most of the studies on mono helical piles were focused on granular soils and few studies were on clayey soils. However, mono helical piles in clayey soils under combined loading remain to be examined. Hence, a series of three-dimensional finite element analyses were carried out to predict the uplift and lateral capacity of the helical pile embedded in soft clay. The numerical model is verified using the results from the analytical results and a small-scale laboratory test. The verified model is used to simulate the helical pile behavior under the combined uplift and lateral loading condition considering the pile with a different number of helical plates. The results of the combined loading analyses reveal that the lateral capacity decreased when the pile was subjected to uplift load, and a maximum reduction of 12% is observed in mono helical piles provided with a single plate for an applied 50% of the ultimate uplift load. The influence of uplift load also increased the bending moment of the helical pile. Finally, it is suggested that the helical piles should be designed considering the aspects for combined loading conditions.

Probabilistic-based nonlinear stability analysis of randomly reinforced microshells under combined axial-lateral load using meshfree strain gradient formulations

In the present exploration, an effective numerical strategy is developed to examine for the first time different microstructural-dependent features in the nonlinear stability behavior of nanocomposite microshells containing randomly dispersed nanofillers under combinations of axial and lateral compressive loads. Correspondingly, the modified strain gradient theory of elasticity incorporating dilatation, deviatoric stretch, and rotation gradient tensors is applied to the third-order shear flexible shell framework to accommodate the size dependency. The efficacious material properties are captured via Tsai homogenization approach together with a Monte-Carlo simulation based upon a probabilistic-based homogenization scheme. By employing the constructed moving Kriging meshfree-based numerical strategy, the essential boundary conditions are directly enforced at nodes and the Kronecker delta is satisfied comprehensively using correct type of moving Kriging shape function. For the combined loading condition having domination of axial compression, it is seen that by taking a lateral compressive load into account, the region of snap-through experience becomes wider and the associated minimum load switches to a more induced deflection, while a smaller shortening. Furthermore, for particular values of volume fraction and specific area of graphene nanofillers, combining of axial or lateral compressive load causes that the roles of microscale-dependent gradient tensors in the value of critical stability loads of combined compressed microsized shells becomes a bit less.

Numerical simulations of Quasi-Static Fracture Behaviour of AISI 316 for Nuclear Transport packages

Nuclear transport packages must pass stringent post-design safety tests before they can be licensed for use. Impact and thermal tests are designed to replicate the worst case conditions in the event of an accident, and often result in the failure of some materials. The outer construction of nuclear transport packages relies on AISI 316. Finite element (FE) models help demonstrate part of the testing required for the performance of nuclear transport packages. FE codes accurately predict the elastic-plastic response of materials up to the ultimate tensile strength. In this study, preliminary work of a series of 12 specimens are designed for numerical simulations using the FE code ABAQUS on AISI 316. The evolution of stress triaxiality during multiaxial loading conditions such as tensile, compressive, pure shear and combined loading conditions is used to further understand ductile fracture.

Influence of dynamic disturbance on rock creep from time, space and energy aspects

In order to explore the influence of dynamic disturbance on creep behavior of rock, the creep damage evolution in rock under the dynamic disturbance are reproduced with creep damage model. In this model, the constitutive law of rock under combined creep and dynamic loading condition is implemented based on elastic damage principle and Norton-Bailey equation in COMSOL Multiphysics. The numerical results show that the dynamic disturbance alters the creep behavior of rock in three aspects, i.e., time, space and energy. In temporal aspect, dynamic disturbance not only accelerates the creep damage evolution of rock, but also leads to the tensile damage accounting for the main damage mode. The tensile damage mode mainly occurs during the unloading stage of dynamic disturbance, and the tendency of transition becomes evident under more dynamic disturbances. In spatial aspect, the dynamic disturbance may facilitate the development of rock damage, resulting in unstable rock failure. In energy aspect, the dynamic disturbance causes creeping rock to absorb and release energy in a short time, which can be quantified with the energy dissipation rate. The residual deformation caused by the dynamic disturbance is also exponentially related to the energy dissipation rate.

Deformation and mechanical responses of AZ31B magnesium alloy under combined shear-compression loading conditions

This work presents a test method and the analytical procedure for materials under complex stress/strain state without the expensive multi-axis experimental machine. The deformation and mechanical responses of Mg alloy under combined shear-compression loading are investigated through a specific loading device. The deformation process and strain path of specimens with various loading angles are discussed based on digital image correlation (DIC) technology. Results show that the combined strain/stress state can be obtained through introducing the additional shear component. However, the loading angle almost has no effect on strain/stress path. In addition, the traditional testing machine equipped with combined loading device provides a new method to carry out the proportional loading test. A modified yield criterion considers Tresca-type material and tension-compression asymmetry is proposed to capture the mechanical characteristics of AZ31b Mg alloy. Based on the investigation, the combined test procedure can be regards as an ideal method in creation of materials database which focus on accurate description about the mechanical and fracture behaviors of materials.

In-depth field survey of a rockslide detachment surface to recognise the occurrence of gravity-induced cracking

This work describes field evidence of gravity-induced cracking that has been identified on the failure scar of a small rockslide (volume = 6–7 m3) that occurred in March 2004 in the Rosandra Valley near the town of Trieste (north-eastern Italy). This shallow rock slope failure involved a limestone slope that was re-profiled through blasting about 135 years ago for the construction of an old railway, which has now been reconverted into a cycle path. Field observations ascertained that the slope failure was characterised by a cascading rupture process in which adjacent blocks collapsed in rapid sequence as a result of the progressive breakage of a number of rock bridges (domino-like collapse), thus highlighting a progressive failure mechanism. The rock bridges were localised in eccentric positions on lateral and rear release planes and failed in tension as a result of combined tensile and bending loading conditions (tensile strength of intact rock = 5 ± 2 MPa). The rockslide was triggered by cyclic loading related to freeze-thaw (ice jacking) that occurred over some consecutive days of daily snowmelt and nocturnal frost. The recognition of newly formed fractures also proves the current progressive development of 3D rupture surfaces of some unstable blocks susceptible to failure. This study provides innovative content to detect gravity-induced cracking in the field, which is an important precursory sign relating to the progressive failure of rock slopes. Gravity-induced cracks can be distinguished from pre-existing discontinuities for their more irregular profile (zigzag pattern), rougher surface, lower persistence and potentially different orientation. This study also provides some new insights into the step-path failure process of steep rock slopes. The mechanical process of initiation, growing and coalescence of gravity-induced fractures is strongly time- and stress-dependent. In the absence of external changing factors that profoundly modify the acting stress state (for instance, engineering countermeasures), progressive failure is a dynamic and irreversible process. For excavated slopes, the creation of a new rock face may abruptly provide the kinematic freedom of potentially unstable blocks, thus determining a very quick stress redistribution. If the mechanical system is not able to redistribute the stress on resisting stiff parts without overcoming the intact rock strength, gravity-induced cracking initiates and propagates until reaching slope collapse within times that are much shorter (from hours to 100–200 years) compared to natural rock slopes subjected to long-lasting geological processes (from 1000 to 2000 up to 10,000–20,000 years).

Creep characterization and modelling of ordinary refractory ceramics under combined compression and shear loading conditions

Creep behaviour of ordinary refractory ceramics is evidently asymmetric under uniaxial tension and compression. In service, they are often exposed to multiaxial stress states. In the present paper, the modified shear test specimens were applied for a creep study in the shear-compression zone of the p-q diagram, and the pure shear creep parameters following the Norton-Bailey strain hardening equation were inversely identified in combination with a weighting function between pure shear and uniaxial compressive conditions. The weighting function was implemented in an in-house asymmetric creep constitutive model. The experimental curves can be well predicted with identified parameters of the asymmetric creep constitutive model. It shows that the shear creep of ordinary refractory ceramics is evidently different to uniaxial compressive/tensile creep. Consideration of shear creep in the thermomechanical modelling of industrial vessels increases the accuracy of simulation results and supports the lining concept optimization investigation.

Modelling and Analysis of High-Speed Angular Contact Ball Bearing

Angular contact bearings are of primal importance in accommodating rotational mechanisms with high-speed characteristics. Their applications are centric to heavy axial and radial loads sustaining thrust loads to a single direction. In high-speed applications, factors such as centrifugal force, gyroscopic moments and relative displacements in various geometric features of the bearings are to be taken into consideration. This study focuses on establishing the contact angles, contact forces and spin speed for angular contact bearing to withstand varied rotational angular velocities. The forces experience a non-linear variation with respect to the body stiffness thus necessitating the involvement of numerical methods to converge at precise solutions through each juncture. The outer raceway of the bearing is accepted to be static with respect to the inner raceway as the input shaft for any application is predominantly affixed to the inner raceway of the angular contact bearing. Geometrical variations are determined under combined load conditions to simulate the natural working of the bearing at accelerated speeds. The analyses involve results for spatial parameters which are iteratively solved for each of the rolling elements in the bearing taken into concern. The spin speeds of the rolling elements are shown to dampen and exponentially increase with respect to their angular positions. The outputs manifested through this work can be utilized to accurately predict shift of salient design attributes of an angular contact bearings through low and high-speed applications.

Combined electromechanical dynamic fracture behavior of lead zirconate titanate (PZT)

AbstractCoupon specimens of poled and depoled lead zirconate titanate (PZT) are examined under combined stress wave and electric loading conditions. Mode‐I crack initiation and fracture behavior is examined using ultrahigh‐speed imaging and two‐dimensional digital image correlation. The dynamic critical stress intensity factor () is extracted using measured displacement fields ahead of the impulsively loaded crack tip, and compared between poled and depoled plates that were either under no electric field, positive 0.46 kV/mm electric field, or negative 0.46 kV/mm electric field. Poled specimens had a poling direction and applied electric field direction normal to the crack front. The addition of an electric field resulted in a crack‐enhancing effect, where the dynamic fracture toughness of poled specimens under 0.46 kV/mm was almost half that of samples with no electric field. Depoled samples experienced almost no change in dynamic fracture toughness with the addition of an electric field.

Consideration of Fatigue Evaluation of SUS316 and SUS430 Steels under Multiaxial Stresses Combined Internal Pressure and Axial Load using Hollow Cylinder Specimen

This study focuses on discussing fatigue life evaluation method of SUS316 and SUS430 steels under wide ranged proportional multiaxial loading conditions. Fatigue tests under 7 types of loading path which are combined axial stress and inner pressure were carried out using hollow cylinder specimens at room temperature. It has been considered that the proportional loading does not cause additional hardening, however this study shows that the complex loading path causes additional hardening without principal direction change of stress and strain in a cycle. The Itoh-Sakane model which evaluates loading and lives under non-proportional multiaxial fatigue by only considering the maximum and the minimum principal stress or strain and their principal directions. However, this model is also needed to consider middle principal stress because change of the middle principal stress influence fatigue life under current loading paths. Therefore, the Itoh-Sakane model was modified to evaluation fatigue life of SUS316 and SUS430 under combined internal pressure and axial loading conditions.

Near-component testing of materials for cylinder heads to determine thermomechanical fatigue under superimposed high-frequency mechanical loads

Abstract Due to higher combustion chamber temperatures and pressures in efficient combustion engines, both the high-cycle and thermomechanical fatigue loads on service life-critical components, such as the cylinder head, are increasing. Material comparisons and analysis of damage behavior are very expensive and time-consuming using component tests. This study therefore develops a test method for cylinder head materials that takes into account the combined loading conditions from the above-mentioned loads and allows realistic temperature transients and gradients on near-component samples. The near-component cylinder head sample represents the failure-critical exhaust valve crosspiece and is tested in a test rig specially designed with the aid of conjugate heat transfer simulations. In the test rig, the sample is subjected to thermal stress by a hot gas burner and to mechanical stress by a high-frequency pulsator. Optical crack detection allows permanent observation of fatigue crack growth and crack closure during the test. Fractographic and metallo-graphic examinations of the fracture areas as well as analyses of the damage patterns show that loads close to engine operation can be set in this way and their influences on the damage can be monitored.

Assessment of the interaction of corrosion defects on steel pipelines under combined internal pressure and longitudinal compression using finite element analysis

Extensive parametric three-dimensional elasto-plastic finite element analyses are carried out to investigate the interaction effect on the burst capacity of oil and gas pipelines containing closely-spaced corrosion defects under combined internal pressure and load-controlled longitudinal compression. The analysis considers two identical, semi-ellipsoidal-shaped corrosion defects aligned circumferentially or longitudinally on the pipeline. The analysis results reveal that the interaction between circumferentially-aligned defects under combined loads is marked: the burst capacity corresponding to the two-defect case can be lower than that corresponding to the single-defect case by as much as 18% as a result of the enhanced bulging of the defect region due to the presence of the longitudinal compression. This is in direct contrast to the observation that the interaction effect is marginal for circumferentially-aligned defects subjected to internal pressure only. On the other hand, the interaction between longitudinally-aligned defects under combined loads is negligible due to the so-called shielding effect; this is again in direct contrast to the observation that the interaction between longitudinally-aligned defects under internal pressure only is marked. The adequacy of four practical interaction rules, which are developed for the loading condition of internal pressure only, for the combined loading condition is also examined. The findings of this study have important practical implications for the integrity assessment of corroded pipelines under combined loads.

A computational framework for meso and macroscale analysis of structural masonry

In this study a computational framework is outlined for modeling the mechanical response of structural masonry at both meso and macroscale. The mesoscale approach accounts for the presence of distinct constituents (i.e., bricks and mortar joints) and their geometric arrangement. A constitutive law with embedded discontinuity, combined with the level-set approach, is used to model the onset and discrete propagation of localized damage in these constituents. The approach is verified against a range of experimental data published in the literature. It is shown that the proposed framework can adequately predict the load-deformation response, as well as the fracture pattern under combined loading conditions. The macroscale approach incorporates the notion of anisotropy parameter whose value depends on the orientation of the principal stress axes in relation to the axes of material symmetry. The material parameters/function appearing in this approach are identified from the ‘virtual data’ generated by a mesoscale analysis of masonry panels subjected to biaxial tension–compression at different orientations of the bed joint. Thus, the mesoscale considerations serve as a bridge for upscaling to the macrolevel.

Structural performance of geopolymer-concrete-filled steel tube members subjected to compression and bending

Materials research has shown geopolymer concrete has the potential to significantly improve the sustainability of concrete construction. In this study, the structural performance of geopolymer concrete-filled steel tube members to take advantage of the beneficial confinement from the outer steel tubes is investigated experimentally and numerically. Experiments on eleven geopolymer concrete-filled steel tube specimens with either square or circular sections subjected to compression, flexure or combined loading conditions are presented. The experimental results, including the ultimate strength, load-deformation responses and failure modes, are obtained and also used as the basis for the validation of a finite element model which is subsequently used to perform parametric studies on the structures with varying cross-sectional dimensions, steel yield strength and member slenderness ratios. The experimental and numerical results are also used to evaluate the applicability of existing design standards for geopolymer concrete-filled steel tube members under combined compression and bending. The evaluation shows that the design approaches developed for ordinary Portland concrete-filled steel tubes in existing standards provide conservative strength predictions for the structures with the geopolymer concrete infill and can therefore be directly applied for safe structural design.

Three-Dimensional Buckling Analysis of Functionally Graded Saturated Porous Rectangular Plates under Combined Loading Conditions

The present work studies the buckling behavior of functionally graded (FG) porous rectangular plates subjected to different loading conditions. Three different porosity distributions are assumed throughout the thickness, namely, a nonlinear symmetric, a nonlinear asymmetric and a uniform distribution. A novel approach is proposed here based on a combination of the generalized differential quadrature (GDQ) method and finite elements (FEs), labeled here as the FE-GDQ method, while assuming a Biot’s constitutive law in lieu of the classical elasticity relations. A parametric study is performed systematically to study the sensitivity of the buckling response of porous structures, to different input parameters, such as the aspect ratio, porosity and Skempton coefficients, along with different boundary conditions (BCs) and porosity distributions, with promising and useful conclusions for design purposes of many engineering structural porous members.

Experimental verification of new features of bearing operation under combined loading conditions

Bearing units of lifting machines, products of construction, road, aviation, space and other branches of technology are very important structural elements, since the failure of even one bearing can cause the failure of the entire product. The results of experimental verification of the theoretical model of bearing operation under combined loading conditions are presented. The behavior under load of bearing units in the most general case can be represented by a sequence of five design schemes, expressed in the form of five statically indeterminate beams. The purpose of the experiments was to test this model under real loading conditions. The experiments were based on the analysis of the geometric shape of the curved elastic line, which the shaft of the bearing assembly acquires under load. The experimental results confirmed the validity of the model and showed that the previously generally accepted model of a two-support beam is not implemented. The conclusion is confirmed that in responsible lifting machines, as well as in responsible products of construction, road, aviation, space and other branches of technology, it is impractical to calculate bearings according to the traditional method, since an erroneous value of bearing durability can be obtained, overestimated from 28.37 to 26.663.9 times.

Stochastic analysis of failure pressure in reinforced thermoplastic pipes under axial loading and external pressure

Reinforced thermoplastic pipes (RTPs) are flexible composite pipes that are acknowledged as a good alternative to conventional submarine pipes. This study aims at investigating the impact of the uncertainties involved in the production process of the RTPs on the failure pressure under combined loading conditions. The stress distributions of RTPs were analyzed using the theory of the three-dimensional (3D) thick-walled cylinder method, combined with the homogenization method. Based on these results, to evaluate the failure mechanisms of RTPs, the 3D Hashin–Yeh failure criterion and the damage evolution model were adopted to establish a progressive failure model. For analyzing the influence of randomness of the related parameters on the first-ply failure (FPF) pressure as well as the final burst failure (FF) pressure of RTPs, a sufficient number of samples were generated using the Monte-Carlo method. Results of the stochastic analysis were validated using the hydraulic burst test data. The statistical evaluation of the stochastic analysis results was performed by using the Weibull probability density distribution function, and the results showed an increase in the probability of getting a lower failure pressure of RTPs than the average failure pressure (considering the randomness of production parameters).

Theoretical substantiation of new features of rolling bearings operation under combined loading conditions

Rolling bearings are widely used in the products of aviation and space technology. To ensure their long-term trouble-free operation, it is necessary to have accurate and reliable information about the forces acting on the bearings. The required values of forces and, accordingly, the required durability of bearings are usually determined on the basis of the traditional design scheme of a double-support beam (smooth beam mounted on two hinged supports). The paper presents a new interpretation of the features of the operation of bearing units on ball radial single-row bearings installed according to the cross located arrangement. It is shown that under conditions of combined loading, including radial and axial forces, the generally accepted theoretical model of a doublesupport beam is not implemented. There is no single calculation model that adequately reflects the nature of the interaction of bearing parts over the entire range of external loads. In the most general case, this model can be represented by a sequence of five statically indeterminate calculation schemes, which are modified and transformed into one another. So, with an increase in the external radial force, the cantilevered beam with additional hinge support scheme is first implemented, which, then, is transformed into the double-sided jamming scheme, and that, later, is transformed into the two double hinge supports scheme. It is also possible to implement two intermediate transition schemes. A specific example shows that in the products of aviation and space technology, determining the durability of bearings based on the traditional model is not advisable, since it can give an overestimated value with an error of 28,37 to 26663,9 times.

Experimental study on creep of double-rock samples disturbed by dynamic impact

During underground mining, rock deformation may be time-dependent and is reflected in rheological behavior. These changes may be also accelerated by dynamic disturbances, such as rock blasting, which can trigger mining-induced hazards such as rockburst and a falling roof. A combined double-rock sample was analyzed to clarify the rockburst mechanism resulting from interaction between roof and pillar. In this work, a double-rock sample was subjected to a combined creep and dynamic loading condition. Based on the results, an ideal mechanical model was developed to describe the interaction between double rock samples loaded in series to simulate interaction between the pillar and roof. To test the model, a double-rock sample composed of granite and sandstone was loaded in series under creep and dynamic loading and the effect of dynamic disturbance on the creep process was quantified. Under the same creep stress, a higher impact dynamic disturbance resulted in shorter failure time. Under the same dynamic disturbance, the specimen failed faster with increased strain energy of rebound of the granite sample under increasing creep stress. The energy dissipation rate and energy transfer efficiency are defined to quantify the energy dissipation of double-rock sample and energy transfer between strong and weak sample. Based on the quantification of energy transfer efficient, it confirms that the ratio of stiffness of the double-rock sample should be a indicator for the energy transfer between strong and weak samples. The granite sample had higher uniaxial compressive strength, so it did not fail during the loading process. For the plaster-granite sample, the granite released most energy to accelerate the unstable failure of plaster. The granite-granite sample failed simultaneously and released most strain energy violently. The results can provide a reference to evaluate the delayed rockburst of rock subjected to creep stress.