Mechanics of materials approach of strength


MECHANICS OF MATERIALS APPROACH TO STRENGTH 3.5.1 Introduction  [c.163]

MECHANICS OF MATERIALS APPROACH TO STRENGTH 3.5.1 Introduction  [c.163]

The whole gamut of topics from micromechanics and macromechanics through lamination theory and examples of plate bending, buckling, and vibration problems is treated so that the physical significance of the concepts is made clear. A comprehensive introduction to composite materials and motivation for their use in current structural applications is given in Chapter 1. Stress-strain relations for a lamina are displayed with engineering material constants in Chapter 2. Strength theories are also compared with experimental results. In Chapter 3, micromechanics is introduced by both the mechanics of materials approach and the elasticity approach. Predicted moduli are compared with measured values. Lamination theory is presented in Chapter 4 with the aid of a new laminate classification scheme. Laminate stiffness predictions are compared with experimental results. Laminate strength con-  [c.539]

The whole gamut of topics from micromechanics and macromechanics through lamination theory and examples of plate bending, buckling, and vibration problems is treated so that the physical significance of the concepts is made clear. A comprehensive introduction to composite materials and motivation for their use in current structural applications is given in Chapter 1. Stress-strain relations for a lamina are displayed with engineering material constants in Chapter 2. Strength theories are also compared with experimental results. In Chapter 3, micromechanics is introduced by both the mechanics of materials approach and the elasticity approach. Predicted moduli are compared with measured values. Lamination theory is presented in Chapter 4 with the aid of a new laminate classification scheme. Laminate stiffness predictions are compared with experimental results. Laminate strength con-  [c.537]

In Chapter 1 the general mechanical properties of plastics were introduced. In order to facilitate comparisons with the behaviour of other classes of materials the approach taken was to refer to standard methods of data presentation, such as stress-strain graphs, etc. However, it is important to note that when one becomes involved in engineering design with plastics, such graphs are of limited value. The reason is that they are the results of relatively shortterm tests and so their use is restricted to quality control and, perhaps, the initial sorting of materials in terms of stiffness, strength etc. Designs based on, say, the modulus obtained from a short-term test would not predict accurately the long-term behaviour of plastics because they are viscoelastic materials. This viscoelasticity means that quantities such as modulus, strength, ductility and coefficient of friction are sensitive to straining rate, elapsed time, loading history, temperature, etc. It will also be shown later that the manufacturing method used for the plastic product can create changes in the structure of the material which have a pronounced effect on properties. The behaviour of the moulded product may therefore be different from the behaviour of a moulded test-piece of the same material.  [c.41]

The mechanics of materials (or strength of materials or resistance of materials) approach embodies the usual concept of vastly simplifying assumptions regarding the hypothesized behavior of the mechanical system. The elasticity approach actually is at least three approaches (1) bounding principles, (2) exact solutions, and (3) approximate solutions.  [c.122]

The mechanics of materials (or strength of materials or resistance of materials) approach embodies the usual concept of vastly simplifying assumptions regarding the hypothesized behavior of the mechanical system. The elasticity approach actually is at least three approaches (1) bounding principles, (2) exact solutions, and (3) approximate solutions.  [c.122]

In order to form floes the individual particles must move and coUide. Flocculation can be classified as either orthokinetic or perikinetic. In the first case particle motion results from turbulence in the suspension, and in the latter from Brownian motion (29). Orthokinetic motion is almost always the case in industrial appHcations. At very close distances, polar materials are attracted by dipole-induced dipole interactions commonly called van der Waals forces. In most aqueous suspensions, ionization of surface groups gives the particle an overall negative charge. The charged particles in suspension are surrounded by a group of positive ions referred to as the double layer. As particles approach each other the resulting electrostatic repulsion of the double layers prevents flocculation. Increasing the ionic strength of the Hquid medium reduces the repulsion until the particles start to aggregate at the critical flocculation concentration. As the charge of these positive ions forming the double layer is increased by adding higher charged ions to the system, the double layer gets nearer to the surface allowing the particles to become closer and be attracted by the van der Waals forces. This is the explanation for the empirically derived Schulze-Hardy rule that the critical flocculation concentration of positive ions for a particular system decreases proportionally with the sixth power of the charge (30). This mechanism is called double-layer compression and is often cited for the inorganic flocculating agents, such as alum and ferric salts, which add trivalent ions to the system. However, this explanation of the action of aluminum and ferric salts does not take into account the fact that they are present at least partially as polymeric species when added to many systems (4), and that polymeric precipitates maybe formed (3) at the usual concentrations and the pH range that they are used.  [c.33]

Of the various physical properties, it is the mechanical properties that make metallic glasses so unique when compared to their crystalline counterparts. A metallic glass obtains its mechanical strength ia quite a different way from crystalline alloys. The disordered atomic stmcture iacreases the resistance to flow ia metallic glasses so that these materials approach their theoretical strength. Strengths of E/50 where E is Young s modulus, are common (Table 2). An attractive feature is that metallic glasses ate equally strong ia all directions because of the random order of their atomic stmcture.  [c.340]

Most measurements of the strength of a material are based on uniaxial stress states. However, the general practical design problem involves at least a biaxial if not a triaxial state of stress. Thus, a logical method of using uniaxial strength information obtained in principal material coordinates is required for analysis of multiaxial loading problems. Obtaining the strength characteristics of a lamina at all possible orientations is physically impossible, so a method must be determined for obtaining the characteristics at any orientation in terms of characteristics in the principal material coordinates. In such an extension of the information obtained in principal material coordinates, the well-known concepts of principal stresses and principal strains are of no value. A multitude of possible microscopic failure mechanisms exists, so a tensor transformation of strengths is very difficult. Moreover, tensor transformations of strength properties are much more complicated than the tensor transformation of stiffness properties. (The strength tensor, if one even exists, must be of higher order than the stiffness tensor.) Nevertheless, tensor transformations of strength are performed and used as a phenomenological failure criterion (phenomenological because only the occurrence of failure is predicted, not the actual mode of failure). A somewhat empirical approach will be adopted the actual failure envelopes in stress space will be compared with simplified failure envelopes.  [c.102]

Most measurements of the strength of a material are based on uniaxial stress states. However, the general practical design problem involves at least a biaxial if not a triaxial state of stress. Thus, a logical method of using uniaxial strength information obtained in principal material coordinates is required for analysis of multiaxial loading problems. Obtaining the strength characteristics of a lamina at all possible orientations is physically impossible, so a method must be determined for obtaining the characteristics at any orientation in terms of characteristics in the principal material coordinates. In such an extension of the information obtained in principal material coordinates, the well-known concepts of principal stresses and principal strains are of no value. A multitude of possible microscopic failure mechanisms exists, so a tensor transformation of strengths is very difficult. Moreover, tensor transformations of strength properties are much more complicated than the tensor transformation of stiffness properties. (The strength tensor, if one even exists, must be of higher order than the stiffness tensor.) Nevertheless, tensor transformations of strength are performed and used as a phenomenological failure criterion (phenomenological because only the occurrence of failure is predicted, not the actual mode of failure). A somewhat empirical approach will be adopted the actual failure envelopes in stress space will be compared with simplified failure envelopes.  [c.102]

The problem of fatigue and fracture prediction for construction materials practically always run into difFiculties connected with low cost effectiveness of experiments, which cannot create the full spectrum of loads and actions existing in reality during service time of the material or structure. The main experiments of failure and fraeture testing use short-time loads and actions. The results of these tests serve for long-time forecast of the material or structure behavior. Such a methodic of using data of short time testing for long-time prediction usually contain a considerable error of fatigue and fracture forecast. It can be explained by the fact that a lot of basic characteristics of materials such as strength, elasticity, plastic flow, micro relaxation, and crack growth process are not able to manifest themselves fully during short-time testing. Fatigue and fracture are non-stationary stochastic processes as during the material or structure service time there are a lot of various unidentified actions bringing about another source of forecast errors. It is especially significant for brittle and elasto-plastic materials, where thermodynamic balance between elastic and plastic properties in time has considerable differences for short and long-time aetions. The majorities of known approaehes, which are used for fatigue physical tests, have deterministic character or use linear stochastic models for materials characterization. This problem is described by differences in building up models for various materials, which have brittle or elasto-plastic properties. It is necessary to note that sometimes the same materials may have different mechanical properties due to impact of different physical actions, such as high temperature, radiation, cryogenic process, etc. That is why it seems to be attractive to find a way for possibility of control and monitoring of materials and structures during their service time. For these purposes it is proposed to use trying loads of materials or structural elements with registration of processes of the material reaction as the AE process. It gives an opportunity to use a system approach for building up models for analysis of the material properties using a short-time behavior.  [c.187]

Significant growth in acrylonitrile end use has come from ABS and SAN resins and adiponittile (see Acrylonitrile polymers). ABS resins are second to acryflc fibers as an outlet for acrylonitrile. These resins normally contain about 25% acrylonitrile and are characterized by thein chemical resistance, mechanical strength, and ease of manufacture. Consumption of ABS resins increased significantly in the 1980s with its growing application as a specialty performance polymer in constmction, automotive, machine, and appliance applications. Opportunities stiU exist for ABS resins to continue to replace more traditional materials for packaging, building, and automotive components. SAN resins typically contain between 25 and 30% acrylonitrile. Because of thein high clarity, they are used primarily as a substitute for glass in drinking cups and tumblers, automobile instmment panels, and instmment lenses. Together, ABS and SAN resins account for about 20% of domestic acrylonitrile consumption. The largest increase among the end uses for acrylonitrile over the past 10 years has come from adiponittile, which has grown to become the third largest outlet for acrylonitrile. It is used by Monsanto as a precursor for hexamethylenediamine (HMDA, CgH N2 [124-09-4]) and is made by a proprietary acrylonitrile electrohydrodimerization process (25). HMD A is used exclusively for the manufacture of nylon-6,6. The growth of this acrylonitrile outlet in recent years stems largely from replacement of adipic acid (C H qO [124-04-9]) with acrylonitrile in HDMA production rather than from a significant increase in nylon-6,6 demand. A non-electrochemical catalytic route has also been developed for acrylonitrile dimerization to adiponittile (26,27,80,81). This technology, if it becomes commercial, can provide additional replacement opportunity for acrylonitrile in nylon manufacture. The use of acrylonitrile for HMD A production should continue to grow at a faster rate than the other outlets for acrylonitrile, but it will not approach the size of the acryflc fiber market for acrylonitrile consumption.  [c.186]

As in other mechanical response phenomena, simple models of a fixed spall strength appear inadequate, and there are no generally agreed upon material-response models. Beyond the usual complexities of shock-compression processes, spall introduces the additional complication of perturbation of global stresses and materials descriptions with local cracking, which can come to dominate the process. With the changes in local stresses resulting from fracture, an internal state variable model approach is perhaps the most realistic to apply [77D02], but has not been fully developed. In any event, failure to consider the consequences of spall can lead to serious discrepancies between predictions and reality.  [c.46]

ConsoHdation is the iatroduction iato a stone s iaterior of a substance which adds extra mechanical strength. Such impregnations have been done usiag both syathetic resias and inorganic compounds. For objects to be stored and exhibited ia a coatroUed iadoor environment, impregnation usiag an organic material may be deemed acceptable. However, for stone objects displayed outdoors, the inherent iastabiHty of the organic materials is a serious drawback to their use. The main practical problems with resia impregnation are the viscosity of the resia solution and the migration of resia to the surface upon solvent evaporation. Many different resias ia various solveats have beea tried, most aotably poly(viayl acetate), poly(methyl methacrylate), other similar acryHcs, and epoxies. Another approach has been to impregnate the stone with epoxy or acryHc monomers and subsequentiy iastigate polymerization in situ.  [c.426]

A combination of siUca derived from siUcon alkoxide and different types of polymers leads to transparent composites having microphase (in the range of 10—100 nm) separation, a higher elastic modulus, and a greater strength than the polymer. Sol—gel siUca-PDMS (polydimethyl sHoxane) hybrids are prepared by in situ precipitation of sol—gel-derived siUca in a swollen PDMS network. The process includes the preparation of a cross-linked PDMS, swelling of the network in tetraethyl orthosiUcate, and precipitation of the siUca by introducing the PDMS filled with TEOS in an aqueous solution containing ethylamine. Mechanical performance of these composites is better than PDMS filled with fumed siUca as in conventional PDMSs. Another approach to the preparation of sol—gel siUca-PDMS hybrids uses the interaction between silanol-terrninated PDMS and silanol groups formed during hydrolysis of TEOS (54). This gives a more homogeneous stmcture, generated by covalent bonds between the siUca network and PDMS chains. The material is optically transparent, showing the absence of macrophase separation, and exhibits a high degree of flexibiUty.  [c.260]

Mechanical Properties. Along with thermal properties, mechanical properties are key to the utihty of engineering plastics. In the majority of apphcations the materials are subject to mechanical stress, often in conjunction with thermal stress. Stiffness and impact strength are among the most desirable properties of a plastic. The first allows for easy and economical design, coming closest to the classical design tradition based on metal properties the second guarantees that the inevitable sudden stresses which everyday articles experience in everyday use will not destroy a given article or prematurely shorten its usefijl lifespan. Frequently, fillers such as glass and other fibers are compounded into plastics to increase their stiffness. Especially in the case of brittle resins this also results in an increase in the tensile and impact strength. To improve impact, special mbber additives of small particle si2e are employed. Typically these impact modifiers are produced by emulsion polymeri2ation and they are almost always copolymers whose outermost layer is composed of a polymer designed to be compatible with the future host resin. Another approach frequently used in impact modification is the chemical reaction of an elastomer, eg, ethylene—propylene—diene, suitably modified to react with the amine functional groups of the polyamide molecule. Impact modifiers are beheved to act by reducing formation of large cracks through cra2e formation, thereby absorbing energy.  [c.265]

A physically well based fracture model that combines a microstmctural approach to fracture with a frracture mechanics failure criterion has been reported. Input data for the model has been acquired from four grades of graphite with widely varying texture. The model and code were successfully benchmarked against H-451 tensile strength data and validated against tensile strength data for grades AGX, IG-110 and AXF-5Q. Two levels of verification were adopted. Initially, the models predictions for the growth of a subcritical defect in H-451 as a function of apphed stress was evaluated and found to be quahtatively correct. Both the initial and final defect lengths were found to decrease with increasing applied stress. Moreover, the sub-critical crack growth required prior to fracture was predicted to be substantially less at higher applied stresses. Both of these observations are qualitatively correct and are readily explained in linear elastic fracture mechanics terms. The probability that a particular defect exists and will propagate through the material to cause failure was also predicted to increase with increasing applied stress. Quantitative validation was achieved by successfiilly testing the model against an experimentally determined tensile strength distribution for grade H-451 graphite. Moreover, the model appeared to qualitatively predict the effect textural changes on the strength of graphite. This was subsequently investigated and the model further validated by testing against three additional graphites, namely grades AGX, IG-110 and AXF-5Q. The versatility and excellent performance of the Burchell fracture model was attributed to its sound physical basis, which recognizes the dominant role of porosity and flaws in the gr aphite fracture process.  [c.531]

Healing, implying the recovery of mechanical strength with time, is primarily due to the diffusion of chains across the interface. The chain diffusion is a special type of mass transfer, which cannot be described by the conventional diffusion equation. Wool and O Connor [13] studied healing of interfaces in terms of the following stages (1) surface rearrangement (2) surface approach (3) wetting (4) diffusion and (5) randomization. By the end of the wetting stage, potential barriers associated with inhomogeneities in the interface disappear and chains are free to move across the interface in the following stages of diffusion and randomization. The latter stages of diffusion and randomization are the most important because the characteristic strength of the polymer material appears in these stages.  [c.356]


See pages that mention the term Mechanics of materials approach of strength : [c.2425]   
Mechanics of composite materials (1999) -- [ c.126 , c.163 , c.164 , c.165 , c.166 , c.167 , c.168 , c.169 , c.170 , c.171 , c.172 , c.173 , c.174 , c.175 , c.176 , c.177 , c.178 , c.179 , c.180 , c.181 , c.182 ]

Machanics of composite materials (1998) -- [ c.126 , c.163 , c.164 , c.165 , c.166 , c.167 , c.168 , c.169 , c.170 , c.171 , c.172 , c.173 , c.174 , c.175 , c.176 , c.177 , c.178 , c.179 , c.180 , c.181 , c.182 ]