Load-deformation curv

The stage is now set to determine the largest load the laminate can carry. Only the outer layers resist the load N after the knee of the load-deformation curve. There, the stress in the outer layers is, from... 

This knee in the load-deformation curve for a plate occurs only for a plate that is perfectly flat before loading. For plates with increasing magnitudes of initial imperfections, the knee is rounded over, and the load-deformation curve decreases as in Figure 5-21. 

The maximum in the curve denotes the stress at yield av and the elongation at yield v. The end of the curve denotes the failure of the material, which is characterized by the tensile strength a and the ultimate strain or elon gation to break. These values are determined from a stress-strain curve while the actual experimental values are generally reported as load-deformation curves. Thus (he experimental curves require a transformation of scales to obtain the desired stress-strain curves. This is accomplished by the following definitions. For tensile tests ... 

Autographic load-deformation curves are often drawn during the test. From such a curve, the modulus of elasticity, proportional limit, and yield strength can be determined,... 

Conventional stress-strain curves are necessarily similar to the load-deformation curves from which they are derived. True stress-strain curves can also be derived in which the stress is based on the actual or installtaueous area of the cross-section. Such curves do not have a maximum corresponding to C, but increase continuously to the breaking load. 

Compression testing can also be carried out at a constant speed. In this case, the applied load, in addition to the deformation of the sample, is monitored. The load-deformation curve for a sample of milk fat (crystallized for 24 hours at 5°C) is shown in Figure 7.9. 

Figure 7.9. Load-deformation curve for a sample of milk fat crystallized at 5°C for 24 hours. S, Fy and ribe refer to the initial stiffness, yield stress and apparent viscosity beyond the yield stress, respectively.

A survey of the load-deformation curves for linear polymers at different temperatures is given in Fig. 25.1A. Each mechanism is further illustrated by a schematic diagram (Figs. 25.1B-E). The mathematical equations for the different mechanisms were given in the Chaps. 13-15. Based on the respective equations Ahmad and Ashby designed Failure Mechanism Maps. The most important of these are reproduced here as Fig. 25.2A-D. 

The compression of uniform samples to the point where the force exceeds the structural capacity causes it to permanently deform and essentially break (4). A typical load-deformation curve can be used to derive values for yield stress, yield strain, and compressive yield work, and depending on the linearity of the onset of compression, a compressive modulus may be obtained (4). These measurements can be used to provide an index of hardness for fats, which have been successfully correlated to the textural attributes of hardness and spreadability obtained through sensory evaluation (4). Unfortunately, these tests are destructive in nature and yield minimal information about the native microstructure of the system. 

Several devices have been developed for the irtrsitu tensile testing of fibres and filaments. To combat the poor sensitivity of the spectrometers, it is usual to strain several fibres simultaneously. Verma and Peterlin looped nylon 6 fibres between two holders, so that the fibres passed through the cavity, with the holders outside the active zone. The holders formed sealed ends to suprasfl quartz tube which could be evacuated to < 10 mm Hg. One holder was fixed, while the other holder was moved by a hand operated screw jack. No provision was made for simultaneously measuring load/deformation curves, which had to be obtained from conventional tensile tests on other fibres. 

Tensile or compressive modulus is the ratio of stress to strain at any point along the initial straight portion of the stress-strain (load-deformation) curve ... 

The compressive strength is calculated by dividing the maximum compressive load by the original minimum cross-sectional area of the specimen. The compressive yield strength is calculated in the same manner, but instead of compressive load at break, the compressive load at the yield point is used. The compressive modulus of elasticity is calculated in the usual manner, by dividing the compressive stress taken as a point on the initial linear portion of the load-deformation curve by the corresponding strain. 

Often, we use a tensile load-deformation curve (see Fig. 3.50) to examine the mechanical behavior of a packaging material. This curve relates the applied load to the resultant deformation of a sample. Commonly, it is measured using an apparatus that provides for a constant slow rate of deformation, and uses a load cell to measure and record the force required to produce that deformation. 

A stress-strain curve (Fig. 3.51) standardizes the load-deformation curve by normalizing the load to a unit cross-sectional area and normalizing the deformation to a unit length. Stress is then the applied tensile load divided by the original cross-sectional area of the specimen, and strain is the increase in length divided by the original length of the sample. 

Figure 10.2 Load deformation curve of Eulaliopsis binata fiber-reinforced green composites.

As shown above, the adhesives with low isocyanate content exhibited good elongation properties, whilst the adhesives formulated with high isocyanate content prepolymers exhibited an initial high slope of the load-deformation curve for the small beech specimens. Both these properties were required for a good performance of the adhesive layer with regard to the plastic model of the engineers. In order to attain the two desired properties, the two polymer types were mixed. 

Load-deformation curves for polyethylene and pofysQrrene are shown in Figure 5.2. Polyethylene necks and cold draws in the manner described above (5.N.1). As it is a semi-crystalline pofymer, yielding involves considerable disruption of the crystal structure. Slip occurs... 

Rice and Skaar [1990] examined AE rates from red oak in green (freshly cut) and partially dried conditions. No AE activity was seen in the green specimens until nonlinearities appeared in the load-deformation curve, immediately prior to rupture. Dried specimens, however, exhibited the classic AE activity previously discussed and illustrated in Fig. 12.2. 

The flexural modulus is the ratio, within the elastic limit, of stress to the corresponding strain. The flexural modulus is the primary means of measuring the stiffness of a material. It is calculated by drawing a tangent to the steepest initial straight-line portion of the load-deformation curve and calculating the following equation ... 

Fig. 1.52 Load-deformation curves of 3D Carbon reinforced SiC obtained by tensile tests [7]. With kind permission of Professor Chetan Sharma Editor in Chief...

An idea of the impact energy associated with these types of failure can be ascertained by consideration of a typical load-deformation curve. This in general will be of the form shown in Figure 18.26. From the definitions given previously a brittle-type failure will occur on the initial, essentially linear part of the curve, prior to the yield point. A... 

Figure 18.26 Typical load deformation curve. Source Author s own files)...

In meshes with a rectangular pattern the reinforcement area Sr is divided into transversal and longitudinal directions Sr = Srj- + Sr. The value of the ultimate matrix strain is difficult to determine because it is related to the definition of a crack. It is generally admitted that for a non-reinforced matrix = 100 - 200.10 . The first deviation from the linear behaviour as observed on the stress-strain or load-deformation curves for ferrocement elements corresponds to = 900 - 1500.10 , but these values are strongly influenced by the volume and type of reinforcement. It has been proved that thinner wires, densely distributed, perform better than thicker ones. 

The tests of the specimens under compressive load proved a considerable increase of bearing capacity due to fibres. The descending branch of the load-deformation curve is long and its shape is strongly related to the kind of fibres used. In the case of elastic fibres a quasi-linear behaviour is observed, but for ordinary polymeric fibres the elastic quasi-plastic behaviour should be expected. Thanks to the artificial cohesion, the reinforced sand is used for construction of walls and slopes with steep gradients between 60° and 90° also in various geotechnical works (Aldea 2007). 

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