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1.
Abstract

Objectives: The purpose of the present study was to evaluate the distribution and magnitude of stresses through the bone tissue surrounding Morse taper dental implants at different positioning relative to the bone crest. Materials and Methods: A mandibular bone model was obtained from a computed tomography scan. A three-dimensional (3D) model of Morse taper implant-abutment systems placed at the bone crest (equicrestal) and 2?mm bellow the bone crest (subcrestal) were assessed by finite element analysis (FEA). FEA was carried out on axial and oblique (45°) loading at 150 N relatively to the central axis of the implant. The von Mises stresses were analysed considering magnitude and volume of affected peri-implant bone. Results: On vertical loading, maximum von Mises stresses were recorded at 6-7?MPa for trabecular bone while values ranging from 73 up to 118?MPa were recorded for cortical bone. On oblique loading at the equiquestral or subcrestal positioning, the maximum von Mises stresses ranged from 15 to 21?MPa for trabecular bone while values at 150?MPa were recorded for the cortical bone. On vertical loading, >99.9vol.% cortical bone volume was subjected to a maximum of 2?MPa while von Mises stress values at 15?MPa were recorded for trabecular bone. On oblique loading, >99.9vol.% trabecular bone volume was subjected to maximum stress values at 5?MPa, while von Mises stress values at 35?MPa were recorded for >99.4vol.% cortical bone. Conclusions: Bone volume-based stress analysis revealed that most of the bone volume (>99% by vol) was subjected to significantly lower stress values around Morse taper implants placed at equicrestal or subcrestal positioning. Such analysis is commentary to the ordinary biomechanical assessment of dental implants concerning the stress distribution through peri-implant sites.  相似文献   

2.
The ability to assess the elastic and failure properties of cortical bone at the radial diaphysis has a clinical importance. A new generation of quantitative ultrasound (QUS) devices and peripheral quantitative computed tomography (p-QCT) has been developed to assess non-invasively bone material and structural properties at the distal radius. This anatomical site is characterized by a thin cortical thickness that complicates traditional mechanical testing methods on specimens. Until now, mechanical properties of cortical bone at distal radius (e.g., elastic modulus, yield stress and strain) remain rarely studied probably due to experimental difficulties. The present study introduces an inverse finite-element method strategy to measure the elastic modulus and yield properties of human cortical specimens of the radial diaphysis. Twenty millimeter-thick portions of diaphysis were cut from 40 human radii (ages 45-90) for biomechanical test. Subsequently the same portion was modeled in order to obtain a specimen-specific three dimensional finite-element model (3D-FEM). Longitudinal elastic constants at the apparent level and stress characterizations were performed by coupling mechanical parameters with isotropic linear-elastic simulations. The results indicated that the mean apparent Young's modulus for radial cortical bone was 16 GPa (SD 1.8) and the yield stress was 153 MPa (SD 33). Breaking load was 12,946 N (SD 3644), cortical thickness 2.9 mm (SD 0.6), structural effective strain at the yield (epsilon(y)=0.0097) and failure (epsilon(u)=0.0154) load were also calculated. The 3D-FEM strategy described here may help to investigate bone mechanical properties when some difficulties arise from machining mechanical sample.  相似文献   

3.
Residual stress due to shrinkage of polymethylmethacrylate bone cement after polymerisation is possibly one factor capable of initiating cracks in the mantle of cemented hip replacements. No relationship between residual stress and observed cracking of cement has yet been demonstrated. To investigate if any relationship exists, a physical model has been developed which allows direct observation of damage in the cement layer on the femoral side of total hip replacement. The model contains medial and lateral cement layers between a bony surface and a metal stem; the tubular nature of the cement mantle is ignored. Five specimens were prepared and examined for cracking using manual tracing of stained cracks, observed by transmission microscopy; cracks were located and measured using image analysis. A mathematical approach for the prediction of residual stress due to shrinkage was developed which uses the thermal history of the material to predict when stress-locking occurs, and estimates subsequent thermal stress. The residual stress distribution of the cement layer in the physical model was then calculated using finite element analysis. Results show maximum tensile stresses normal to the observed crack directions, suggesting a link between residual stress and pre-load cracking. The residual stress predicted depends strongly on the definition of the reference temperature for stress-locking. The highest residual stresses (4-7 MPa) are predicted for shrinkage from maximum temperature; in this case, magnitudes are sufficiently high to initiate cracks when the influence of stress raisers such as pores or interdigitation at the bone/cement interface are taken into account (up to 24 MPa when calculating stress around a pore according to the method of Harrigan and Harris (J. Biomech. 24(11) (1991) 1047-1058). We conclude that the damage accumulation failure scenario begins before weight-bearing due to cracking induced by residual stress around pores or stress raisers.  相似文献   

4.
Residual stress and strain in living tissues have been investigated from the viewpoint of mechanical optimality maintained by adaptive remodeling. In this study, the residual stresses in the cortical-cancellous bone complex of bovine coccygeal vertebrae were examined. Biaxial strain gages were bonded onto the cortical surface, so that the gage axes were aligned in the cephalocaudal and circumferential directions. Strains induced by removal of the end-plate and the cancellous bone were recorded sequentially. The results revealed the existence of compressive residual stress in the cortical bone and tensile residual stress in the cancellous bone in both the cephalocaudal and the circumferential direction. The observed strains were examined on the basis of the uniform stress hypothesis using a three-bar model for the cephalocaudal direction and a three-layered cylinder model for the circumferential direction. In this model study, the magnitude of effective stresses, which is defined as the macroscopic stress divided by the area fraction of bone material, was found not to differ significantly between cephalocaudal and circumferential directions, although they were evaluated using independent models. These results demonstrate that the uniform stress state of the cortical-cancellous bone structure is consistent with results obtained in the cutting experiment when the existence of residual stress is taken into account.  相似文献   

5.
The presence of the residual stresses in bone tissue has been noted and the authors have reported that there are residual stresses in bone tissue. The aim of our study is to measure the residual stress distribution in the cortical bone of the extremities of vertebrates and to describe the relationships with the osteon population density. The study used the rabbit limb bones (femur, tibia/fibula, humerus, and radius/ulna) and measured the residual stresses in the bone axial direction at anterior and posterior positions on the cortical surface. The osteons at the sections at the measurement positions were observed by microscopy. As a result, the average stresses at the hindlimb bones and the forelimb bones were 210 and 149 MPa, respectively. In the femur, humerus, and radius/ulna, the residual stresses at the anterior position were larger than those at the posterior position, while in the tibia, the stress at the posterior position was larger than that at the anterior position. Further, in the femur and humerus, the osteon population densities in the anterior positions were larger than those in the posterior positions. In the tibia, the osteon population density in the posterior position was larger than that in the anterior position. Therefore, tensile residual stresses were observed at every measurement position in the rabbit limb bones and the value of residual stress correlated with the osteon population density (r=0.55, P<0.01).  相似文献   

6.
Periprosthetic osteolysis in the retroacetabular region with cancellous bone loss is a recognized phenomenon in the long-term follow-up of total hip replacement. The effects on load transfer in the presence of defects are less well known. A finite element model incorporating a retroacetabular defect behind a cementless component was validated against a 4th generation sawbone pelvis. Computational predictions of surface strain and von Mises stresses were closely correlated to experimental findings. The presence of a cancellous defect increased von Mises stress in the cortical bone of the medial wall of the pelvis. At a load of 600 N this was under the predicted failure stress for cortical bone. Increases in the cup size relative to the acetabulum caused increased stress in the cortical bone of the lateral wall of the pelvis, adjacent to the acetabulum. We are confident that our modeling approach can be applied to patient specific defects to predict pelvis stress with large loads and a range of activities.  相似文献   

7.
The objective of this study was to assess mechano-biological response of articular cartilage when subjected to a single impact stress. Mature bovine cartilage explants were impacted with peak stresses ranging from 10 to 60 MPa at a stress rate of 350 MPa/s. Water loss, matrix axial deformation, dynamic impact modulus (DIM), and cell viability were measured immediately after impaction. The water loss through the articular surface (AS) was small and ranged from 1% to 6% with increasing peak stress. The corresponding axial strains ranged from 2.5% to 25%, respectively, while the DIM was 455.9 +/- 111.9 MPa. Chondrocyte death started at the articular surface and increased in depth to a maximum of 6% (70 microns) of the cartilage thickness at the highest stress. We found that the volumetric (axial) strain was more than twice the amount of water loss at the highest peak stress. Furthermore, specimens impacted such that the interstitial water was forced through the deep zone (DZ) had less water loss, a higher DIM, and no cell death. These findings appear to be due to matrix compaction in the superficial region causing higher compressive strains to occur at the surface rather than in the deeper zones.  相似文献   

8.
Short and long duration tests were conducted on hollow femoral bone cylinders to study the circumferential (hoop) creep response of cortical bone subjected to an intramedullary radial load. It was hypothesized that there is a stress threshold above which nonlinear creep effects dominate the mechanical response and below which the response is primarily determined by linear viscoelastic material properties. The results indicate that a hoop stress threshold exists for cortical bone, where creep strain, creep strain rate and residual strain exhibited linear behavior at low hoop stress and nonlinear behavior above the hoop stress threshold. A power-law relationship was used to describe creep strain as a function of hoop stress and time and damage morphology was assessed.  相似文献   

9.
Mitral annuloplasty has been a keystone to the success of mitral valve repair in functional mitral regurgitation. Understanding the complex interplay between annular-ring stresses and left ventricular function has significant implications for patient-ring selection, repair failure, and patient safety. A step towards assessing these challenges is developing a transducer that can be implanted in the exact method as commercially available rings and can quantify multidirectional ring loading. An annuloplasty ring transducer was developed to measure stresses at eight locations on both the in-plane and out-of-plane surfaces of an annuloplasty ring's titanium core. The transducer was implanted in an ovine subject using 10 sutures at near symmetric locations. At implantation, the ring was observed to undersize the mitral annulus. The flaccid annulus exerted both compressive (−) and tensile stresses (+) on the ring ranging from −3.17 to 5.34 MPa. At baseline hemodynamics, stresses cyclically changed and peaked near mid-systole. Mean changes in cyclic stress from ventricular diastole to mid-systole ranged from −0.61 to 0.46 MPa (in-plane direction) and from −0.49 to 1.13 MPa (out-of-plane direction). Results demonstrate the variability in ring stresses that can be introduced during implantation and the cyclic contraction of the mitral annulus. Ring stresses at implantation were approximately 4 magnitudes larger than the cyclic changes in stress throughout the cardiac cycle. These methods will be extended to ring transducers of differing size and geometry. Upon additional investigation, these data will contribute to improved knowledge of annulus-ring stresses, LV function, and the safer development of mitral repair techniques.  相似文献   

10.
This study aims to investigate the influence of the presence, shape and depth of NCCLs on the mechanical response of a maxillary second premolar subjected to functional and non-functional occlusal loadings using 3-D finite element (FE) analysis. A three-dimensional model of a maxillary second premolar and its supporting bone was constructed based on the contours of their cross-sections. From the sound model, cervical defects having either V- or U-shapes, as found clinically, were subtracted in three different depths. The models were loaded with 105 N to simulate normal chewing forces according to a functional occlusal loading (F1) vertically applied and two non-functional loadings (F2 and F3) obliquely oriented. Two alveolar bone crest heights were tested. Ansys™ FE software was used to compute stress distributions and maximum principal stress for each of the models. The presence of a lesion had no effect on the overall stress distribution of the system, but affected local stress concentrations. Non-functional loadings exhibited tensile stresses concentrating at the cervical areas and root surfaces, while the functional loading resulted in homogeneous stress distributions within the tooth. V-shaped lesions showed higher stress levels concentrated at the zenith of the lesion, whereas in U-shaped defect stresses concentrated over a wider area. As the lesions advanced in depth, the stress was amplified at their deepest part. A trend of stress amplification was observed with decreasing bone height. These results suggest a non-linear lesion progression with time, with the progression rate increasing with patient's age (deeper lesions and lower bone support).  相似文献   

11.
The rate-limiting step in the delivery of nutrients to osteocytes and the removal of cellular waste products is likely diffusion. The transport of osteoid water across the mineralized matrix of bone was studied by proton nuclear magnetic resonance spectroscopy and imaging by measuring the diffusion fluxes of tissue water in cortical bone specimens from the midshaft of rabbit tibiae immersed in deuterium oxide. From the diffusion coefficient (Da = (7.8 ± 1.5) × 10−7 cm2/s) measured at 40°C (close to physiological temperature), it can be inferred that diffusive transport of small molecules from the bone vascular system to the osteocytes occurs within minutes. The activation energy for water diffusion, calculated from Da measured at four different temperatures, suggests that the interactions between water molecules and matrix pores present significant energy barriers to diffusion. The spatially resolved profile of Da perpendicular to the cortical surface of the tibia, obtained using a finite difference model, indicates that diffusion rates are higher close to the endosteal and periosteal surfaces, decreasing toward the center of the cortex. Finally, the data reveal a water component (∼30%) diffusing four orders of magnitude more slowly, which is ascribed to water tightly bound to the organic matrix and mineral phase.  相似文献   

12.
High-energy synchrotron X-ray diffraction was used to study internal stresses in bone under in situ compressive loading. A transverse cross-section of a 12-14 year old beagle fibula was studied with 80.7 keV radiation, and the transmission geometry was used to quantify internal strains and corresponding stresses in the mineral phase, carbonated hydroxyapatite. The diffraction patterns agreed with tabulated patterns, and the distribution of diffracted intensity around 00.2/00.4 and 22.2 diffraction rings was consistent with the imperfect 00.1 fiber texture expected along the axis of a long bone. Residual compressive stress along the bone's longitudinal axis was observed in the specimen prior to testing: for 22.2 this stress equaled -95 MPa and for 00.2/00.4 was between -160 and -240 MPa. Diffraction patterns were collected for applied compressive stresses up to -110 MPa, and, up to about -100 MPa, internal stresses rose proportionally with applied stress but at a higher rate, corresponding to stress concentration in the mineral of 2.8 times the stress applied. The widths of the 00.2 and 00.4 diffraction peaks indicated that crystallite size perpendicular to the 00.1 planes increased from t=41 nm before stress was applied to t=44 nm at -118 MPa applied stress and that rms strain epsilon(rms) rose from 2200 muepsilon before loading to 4600 muepsilon at the maximum applied stress. Small angle X-ray scattering of the unloaded sample, recorded after deformation was complete, showed a collagen D-period of 66.4 nm (along the bone axis).  相似文献   

13.
The reasons for the increase in fracture rates with age are not fully understood. It is known that there is a decrease in bone mass with a presumed loss of strength. This decrease may possibly be compensated for by changes in cross-sectional geometry. Previous studies, which have been limited by lack of information on subjects’ heights and weights, were not able to resolve this issue. In this study, measurements of cross-sectional geometry (area and second moments of area) from 107 specimens of human femoral diaphysis from subjects aged 21–92 years were analysed. Mathematical models of the variation in bone geometry with age were developed. These models included the effects of sex, height and weight. Values of parameters from these models were then used in a biomechanical analysis of the static stresses at the mid-shaft of the femur. Results indicate that although there was a reduction in cortical area in old age, bone tissue was redistributed so that neither bending stresses in the coronal plane nor torsional stresses were higher in old age than in young adulthood. An additional finding was that at any age women had smaller bones, less cortical bone area and higher bone stresses than men. This finding may have some bearing on the higher fracture incidence seen in older women.  相似文献   

14.
The initial fixation of a cemented hip implant relies on the strength of the interface between the stem, bone cement and adjacent bone. Bone cement is used as grouting material to fix the prosthesis to the bone. The curing process of bone cement is an exothermic reaction where bone cement undergoes volumetric changes that will generate transient stresses resulting in residual stresses once polymerization is completed. However, the precise magnitude of these stresses is still not well documented in the literature. The objective of this study is to develop an experiment for the direct measurement of the transient and residual radial stresses at the stem-cement interface generated during cement polymerization. The idealized femoral-cemented implant consists of a stem placed inside a hollow cylindrical bone filled with bone cement. A sub-miniature load cell is inserted inside the stem to make a direct measurement of the radial compressive forces at the stem-cement interface, which are then converted to radial stresses. A thermocouple measures the temperature evolution during the polymerization process. The results show the evolution of stress generation corresponding to volumetric changes in the cement. The effect of initial temperature of the stem and bone as well as the cement-bone interface condition (adhesion or no adhesion) on residual radial stresses is investigated. A maximum peak temperature of 70 degrees C corresponds to a peak in transient stress during cement curing. Maximum radial residual stresses of 0.6MPa in compression are measured for the preheated stem.  相似文献   

15.
Knowledge of the forces that act upon the equine humerus while the horse is standing and the resulting strains experienced by the bone is useful for the prevention and treatment of fractures and for assessing the proximolateral aspect of the bone as a site for obtaining autogenous bone graft material. The first objective was to develop a mathematical model to predict the loads on the proximal half of the humerus created by the surrounding musculature and ground reaction forces while the horse is standing. The second objective was to calculate surface bone stresses and strains at three cross sections on the humerus corresponding to the donor site for bone grafts, a site predisposed to stress fracture, and the middle of the diaphysis. A three-dimensional mathematical model employing optimization techniques and asymmetrical beam analysis was used to calculate shoulder muscle forces and surface strains on the proximal and mid-diaphyseal aspects of the humerus. The active shoulder muscles, which included the supraspinatus, infraspinatus, subscapularis, and short head of the deltoid, produced small forces while the horse is standing; all of which were limited to 4.3% of their corresponding maximum voluntary contraction. As a result, the strains calculated at the proximal cross sections of the humerus were small, with maximum compressive strains of -104microepsilon at the cranial aspect of the bone graft donor cross section. The middle of the diaphysis experienced larger strain magnitudes with compressive strains at the lateral and the caudal aspects and tensile strains at the medial and cranial aspects (-377microepsilon and 258microepsilon maximum values, respectively) while the horse is standing. Small strains at the donor bone graft site do not rule out using this location to harvest bone graft tissue, although strains while rising to a standing position during recovery from anesthesia are unknown. At the site common to stress fractures, small strains imply that the stresses seen by this region while the horse is standing, although applied for long periods of time, are not a cause of fracture in this location. Knowing the specific regions of the middle of the diaphysis of the humerus that experience tensile and compressive strains is valuable in determining optimum placement of internal fixation devices for the treatment of complete fractures.  相似文献   

16.
We reported on quantitative anatomical comparisons of reed culms grown under a wide range of water depth (from −10 to +230 cm). The study focused mainly on the above water parts of ramets, but also provided an insight into the submerged internodes. Investigated anatomical features were: radial thickness of the internode wall and that of each tissue constituting it (epidermis and subepidermal tissues, aerenchyma channels, cortical sclerenchyma and parenchyma); areas of aerenchyma channels and the summed transversal area of them; areas of the innermost vascular bundles involving the bundle sheath sclerenchyma, phloem and metaxylem vessels; the cross-sectional area of the pith cavity and that of the internode wall. After a 2–3% decrease below the uppermost internode, the thickness of internode tissues, except for cortical sclerenchyma, continuously increased downwards. Quantitative differences between the ramets grown at different water depths were observed only from the lower aerial internodes. Parenchyma taking part considerably in the mechanical stability of culms with its large extension and thick cell walls was more-layered and thicker (with the maximum thicknesses of approximately 1200 and 1000 μm) in ramets from 180–200 than from 20–30 cm water depth. Areas of the innermost vascular bundles increased downwards and decreased after a maximum value appearing in lower internodes of ramets grown in deeper than shallower water. Aerenchyma channels appeared farther up from the water surface in culms in shallower than deeper water: the top ends were found about 50 cm higher in culms from 20–30 than from 180–200 cm water depth. Along the transect at right angles to the shore, the radial thickness and area of aerenchyma channels were higher in ramets grown in medium water depth—the summed transversal area of them was greater than 4 mm2 in internodes at the water surface, while plants from the two ends of the water depth gradient had smaller aerenchyma channels (with approximately 1 mm2 total areas). In contrast, pith cavity area at the water surface continuously increased – up to 60 mm2 – from shallower to deeper water. Therefore, oxygen transport in ramets grown at the open water fringe of stands may occur mostly in the pith cavity.  相似文献   

17.
Knowledge of kinetics of fatigue crack growth of microcracks is important so as to understand the dynamics of bone adaptation, remodeling, and the etiology of fatigue-based failures of cortical bone tissue. In this respect, theoretical models (Taylor, J. Biomech., 31 (1998) 587-592; Taylor and Prendergast, Proc. Instn. Mech. Engrs. Part H 211 (1997) 369-375) of microcrack growth in cortical bone have predicted a decreasing microcrack growth rate with increasing microcrack length. However, these predictions have not been observed directly. This study investigated microcrack growth and arrest through observations of surface microcracks during cyclic loading (R=0.1, 50-80MPa) of human femoral cortical bone (male, n=4, age range: 37-40yr) utilizing a video microscopy system. The change in crack length and orientation of eight surface microcracks were measured with the number of fatigue cycles from four specimens. At the applied cyclic stresses, the microcracks propagated and arrested in generally less than 10,000 cycles. The fatigue crack growth rate of all microcracks decreased with increasing crack length following initial identification, consistent with theoretical predictions. The growth rate of the microcracks was observed to be in the range of 5x10(-5) to 5x10(-7)mmcycle(-1). In addition, many of the microcracks were observed not to grow beyond 150 microm and a cyclic stress intensity factor of 0.5MNm(-3/2). The results of this study suggest that cortical bone tissue may resist fracture at the microscale by deceleration of fatigue crack growth and arrest of microcracks.  相似文献   

18.
The interfacial strength of secondary osteons from the diaphysis of the Thoroughbred equine third metacarpal was evaluated using the fiber pushout test. The pushout was performed on 300-500 microm sections of 4x4x15 mm bone blocks machined from four anatomic regions of the cortex. Pushout strength was evaluated from proximal to distal location within the diaphysis on four osteon types classified under polarized light on adjacent histologic sections from each block. The shear strength of the interfaces were estimated from shear lag theory. Differences were found in the interfacial strength of osteons based on appearance under polarized light with bright field having the highest interfacial strength (40.3 MPa). The lowest strength was found in the dark field osteons (22.8 MPa). The dorsal region had the highest shear strength and toughness compared to all other regions. The cement line and interlamellar interfaces are similar in strength, but exhibit regional dependence--specifically, the palmar region strength is less (17.5 MPa) than the osteon interlamellar interfaces (30.4 MPa) and osteon type dependent (alternating significantly weaker than other types). Histomorphometry revealed significant regional differences (p<0.0001) in osteon area fraction among the four osteon types as well as differences in the osteon diameter (p=0.01), with dorsal regions having larger osteons (170 microm) than the palmar region (151 microm). Fatigue life and fracture toughness of Haversian bone are reported in the literature to be regionally dependent and are known to be associated with osteon pullout--an osteon interfacial phenomenon. Therefore, the results presented in this study are important to further the understanding of the mechanisms of fragility and damage accumulation in cortical bone.  相似文献   

19.
This study presents first hand data on the cloning and heterologous expression of Anabaena PCC 7120 all3940 (a dps family gene) in combating nutrients limitation and multiple abiotic stresses. The Escherichia coli transformed with pGEX-5X-2-all3940 construct when subjected to iron, carbon, nitrogen, phosphorus limitation and carbofuron, copper, UV-B, heat, salt and cadmium stress registered significant increase in growth over the cells transformed with empty vector under iron (0%), carbon (0.05%), nitrogen (3.7 mM) and phosphorus (2 mM) limitation and carbofuron (0.025 mg ml−1), CuCl2 (1 mM), UV-B (10 min), heat (47 °C), NaCl (6% w/v) and CdCl2 (4 mM) stress. Enhanced expression of all3940 gene measured by semi-quantitative RT-PCR at different time points under above mentioned treatments clearly demonstrates its role in tolerance against aforesaid abiotic stresses. This study opens the gate for developing transgenic cyanobacteria capable of growing successfully under above mentioned stresses.  相似文献   

20.
Despite its clinical importance, the fatigue behaviour of cortical bone has not been examined as widely as its static behaviour. In the present study, specimens from the tibiae of horses have been subjected to load-controlled single step tests. The cyclic deformation behaviour was described by the development of stress-strain hysteresis parameters over the lifetime. The fatigue behaviour of bone is characterised by cyclic softening which is most distinctive towards the end of the lifetime. The microstructural damage accumulated during cyclic loading results in a loss of stiffness, asymmetrical deformation of the bone in tension and compression in cyclic creep. As shown by light and scanning electron microscopy, microcrack formation and growth is the main damage mechanism. The crack growth behaviour is strongly influenced by the microstructure, the stress components and the absolute value of the local stresses. Lower local stresses and/or compressive mean stresses lead to a dominant influence of the shear stress components with shear failure at inner interfaces. With increasing crack length, that is, higher local stress amplitudes, or tensile mean stresses, the microstructure is more and more ignored and failure occurs primarily under the influence of the normal stress components. This can be clearly seen on the fracture and specimen surfaces.  相似文献   

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