Elastic modulus and strength

In some cases, the elastic modulus of concrete needs to be known. The elastic modulus is determined by the dynamic compressive test in accordance to CEN EN 13412 (2006) or ASTM C 469 (2010). 

The elastic modulus is related to the strength of concrete. The relationships suggested (Nunn 2004) may be used, if the elastic modulus is to be estimated from the strength of cement-bound mixtures (CBMs)  

According to AASHTO (2008), the modulus of elasticity of lean concrete and cement-treated aggregate may be estimated by using the following equation  

The elastic modulus, in contrast to compressive strength, does not noticeably increase with curing time, as it has been found by Croney and Croney (1991) testing specimens produced with crushed aggregates or gravels and cured for up to 520 and 104 weeks, respectively. Moreover, Croney and Croney (1991) state that the computed stresses in the concrete slab are not very sensitive to small changes in the elastic modulus. 

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The elastic modulus and strength are related by a Griffith theory type relationship. 

Resilin and elastin have relatively high extensibility and resilience, but as compared to the collagen and the silks, the proteins sacrifice stiffness (elastic modulus) and strength (see Table 2). Collagen and dragUne sflk are much stiffer materials, but lack the extensibility that is characteristic of the rubber-like proteins. On the other hand, the mussel byssus fibers and the viscid silk have the extensibility of resilin and elastin, but lack the resilience [208]. 

The geometry and structure of a bone consist of a mineralised tissue populated with cells. This bone tissue has two distinct structural forms dense cortical and lattice-like cancellous bone, see Figure 7.2(a). Cortical bone is a nearly transversely isotropic material, made up of osteons, longitudinal cylinders of bone centred around blood vessels. Cancellous bone is an orthotropic material, with a porous architecture formed by individual struts or trabeculae. This high surface area structure represents only 20 per cent of the skeletal mass but has 50 per cent of the metabolic activity. The density of cancellous bone varies significantly, and its mechanical behaviour is influenced by density and architecture. The elastic modulus and strength of both tissue structures are functions of the apparent density. 

As carbon nanotubes present exceptional mechanical, superior thermal and electrical properties in general, by using them as reinforcing elements there are high expectations for improvement of quality of nano- and microcomposites [14-18]. As shown from earlier measurements, through carbon nanotube addition a 15-37% improvement of mechanical properties (elastic modulus and strength) can be achieved in comparison to other carbon-filled samples [19]. 

During the test the cross head displacement is recorded as well as the compression load registered by the load cell. For temperature tests, the temperature is raised slowly (3°C per minute) and once the desired temperature is achieved and settled, the test is commenced. The properties are determined by use of standard equations which for elastic modulus and strength the applicability of the equations were checked by use of finite element stress analysis in these geometries. Strength tests are clearly loaded until fracture occurs, and typical examples show initiation at the centre of the pellets and disintegration into two or three parts. 

The two-component system—crystal lamellae or blocks alternating with amorphous layers which are reinforced by tie molecules— results in a mechanism of mechanical properties which is drastically different from that of low molecular weight solids. In the latter case it is based on crystal defects and grain boundaries. In the former case it depends primarily on the properties and defects of the supercrystalline lattice of lamellae alternating with amorphous surface layers (in spherulitic, transcrystalline or cylindritic structure) or of microfibrils in fibrous structure, and on the presence, number, conformation and spatial distribution of tie molecules. It matters how taut they are, how well they are fixed in the crystal core of the lamellae or in the crystalline blocks of the microfibrils and how easily they can be pulled out of them. In oriented material the orientation of the amorphous component (/,) is a good indicator of the amount of taut tie molecules present and hence an excellent parameter for the description of mechanical properties. In fibrous structure it directly measures the fraction and strength of microfibrils present and therefore turns out to be almost proportional to elastic modulus and strength in the fibre direction. 

Grades reinforced with glass fiber and other materials offer superior elastic modulus and strength... 

Lu and Larock (2007) worked on organomodified MMTs with (4-vinylbenzyl) trie-thylammonium cation to reinforce com oil-based biopolymer. The cation conjunction process was employed to prepare nanocomposites with styrene and divinylbenzene as well as boron trifluoride diethyl etherate modified with fish oil as the initiator, resulting in higher elastic modulus and strength, fracture toughness, and better thermal stability with 2—3 wt% nanoclay inclusions. 

Bend tests are useful for very hard ceramics that cannot be machined to the shapes required for use in a standard tensile testing machine. It has also been applied to measure the elastic modulus and strength of material that is too soft and fragile to be clamped in the testing machine. The elastic modulus and strength of very delicate protein crystals, only a millimeter or so in length, have been measured from which their bond energy was determined. 

Mechanical property measurements of films on substrates are made using the beam deflection techniques discussed under stress measurement except that the beam is loaded with known weights and the deflection is measured with the stress as the known.[ l Measurements can oidy be made as long as the film does not microcrack (tension) or bhster (compression). ] Thin films have been shown to have very high elastic modulus and strength, presumably due to surface pinning of mobile defects (dislocations). An indentation test may be used to determine the elastic properties of coatings. ... 

Although it is not immediately obvious, Eqs. (4) and (5) have the same general dependency on the elastic modulus and strength. When the thermoelastic stress is expressed in simple form for total linear restraint in one dimension, it is of the form... 

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