Stress measurement principal stresses

Measuring points Depth/ni Maximum principle stress Intermediate principal stress Minimum principle stress ... 

The results of an experimental research activity aimed at the system setup of the Stress Pattern Analysis by Measuring Thermal Emission used to measure the sum of the principal stresses of the free surface are presented. 

The SPATE technique is based on measurement of the thermoelastic effect. Within the elastic range, a body subjected to tensile or compressive stresses experiences a reversible conversion between mechanical and thermal energy. Provided adiabatic conditions are maintained, the relationship between the reversible temperature change and the corresponding change in the sum of the principal stresses is linear and indipendent of the load frequency. 

The calibration curve of each rosetta strain gauge was so obtained and ftg.5 shows the sum of the principal stresses at the measuring points versus pressure inside the vessel. Further tests were carried out to obtain the calibration factor and to check that it remained constant on the whole scan area of the test surface. This was achieved through additional measurements using the SPATE system on fixed points on the surface located very close to the applied rosetta strain gauges. This procedure gave the following results ... 

Fig.5 Sum of the principal stresses at the measuring points versus pressure inside the vessel.

Fig.6 Correlator output versus the peak to peak amplitude of the periodic change in the sum of the principal stresses at the measuring point (R5) for an assigned frequency (5Hz).

As shown in Fig. 1, a cubic body of material under consideration is deformed in the directions of orthogonal axes Xt. If this mode of deformation, the coordinate axes coincide with the principal strain axes. In the principal stresses af corresponding to the principal strains are measured as functions of stretch ratios X, in the directions of Xh W can be calculated from... 

In principle, W can be determined from Eq. (2) if principal stresses at are measured as functions of applied principal stretch ratios X,-. However, since bW/bJ/ rather than W itself are more directly connected with the stress-strain relations [see Eq. (11)], their determination from the measurements of at and X,- is more feasible than that of W. 

The molecular deformation ratio K in the directions I and II can be estimated in the following way the difference Aa between the principal stresses in the x-y plane can be readily calculated from the birefringence A (measured parallel and perpendicular to the direction of extinction) and the stress-optical coefficient C for molten polystyrene (C= 4.8xlO Pa , see Chapter III.l). According to the classical network theory, the stress tensor is proportional to the Cauchy deformation tensor which means that the network deformation along the principal directions of the stress tensor are X and 1/ where ... 

Therefore, in the general case, only the sum of the principal stresses can be obtained from such a measurement, and the value of do is again required. 

Although, the powder method was developed as early as 1916 by Debye and Scherrer, for more than 50 years its use was almost exclusively limited to qualitative and semi-quantitative phase analysis and macroscopic stress measurements. The main reason for this can be found in what is known as the principal problem of powder diffraction accidental and systematic peak overlap caused by a projection of three-dimensional reciprocal space on to the one-dimensional 26 axis, leading to a strongly reduced information content compared to a single crystal data set. However, despite the loss of angular information, often sufficient information resides in the ID dataset to reconstruct the 3D structure. Indeed, quantitative analysis of the pattern using modern computers and software yields the wealth of additional information about the sample structure that is illustrated in Figure 1. Modern... 

Then, to have all measures in the same units, we take (sumn) and (summ). To emphasize the difference between the invariants and the principal stresses, we use the symbols S, S, and Thus... 

Figures 6 through 8 show results of the strain gauge experiments on the three different molding compounds A, B, and C. Each of these figures gives the principal stresses and q2 anc The maximum shear stress Tmax as measured in the center and on the corner of the die. These results were obtained after averaging measurements on at least 10 individual die. The results are given as function of the number of cycles in THSK testing. Except for the measurement after 300 cycles the stress levels at all positions after any number of cycles are smaller for material C than for material B. The stresses for material B are comparable to those for material A. The deviant behavior after 300 cycles observed with material A shows a large reduction in stress, indicative of a loss of adhesion. However, the increase observed after 500 cycles cannot be explained if indeed the integrity of the interface has been compromised.

Kee and Durning (1990) reviewed two principal methods of measuring yield stresses dynamic and static methods. One example of the dynamic method is the extrapolation from the flow curve. Equation (4) is often used to determine the yield stress of gum solutions. Table VIII lists the examples of yield stress of several selected food commodities measured from different methods. It is noted that for the same food product, different methods have different yield stress value. In addition to the measuring method, the embedded factor—the composition of food products—also needs to be emphasized. For instance, in mayonnaise, the concentration of oil and xanthan gum significantly affected the yield stress since it increased from... 

The development and dissipation of excess pore water pressures in the vicinity of the advancing tunnel (at the time of the FEBEX tunnel excavation) was a clear example of hydromechanical interaction. It was concluded that the development of pore pressures was controlled by the initial stress field state, by the rate of excavation and by the permeability and drainage properties of the granite. However, the available information on the intensity and direction of principal stresses in the area was found inconsistent with the actual measurements. The problem posed by this discrepancy was essentially unsettled since a precise determination of the initial stress state in the vicinity of the FEBEX tunnel was not available. 

The principal mechanical properties of granite rock matrix were provided for the purposes of this task no mechanical characterization of discontinuities was available. The stress measurements presented by Pahl el al. (1989) show that the stress field is triaxial with horizontal stresses 4 to 5 times higher than the lithostatic pressure and a difference of greater than 10 MPa between the minimum and maximum horizontal stresses (see Figure 3). 

Figure 11.8 shows that the flow can be divided conceptually into three zones a laminar sublayer nearest the pipe wall, in which the shear stress is principally due toj viscous shear a turbulent core in the middle of the pipe, in which the shear stress is principally due to turbulent. Reynolds stresses and a layer between them, called the buffer layer, in which both viscous and Reynolds stresses are of the same order of magnitude. Good experimental measurements are difficult to make in the laminar sublayer and buffer layer, so there is some controversy over the best location for the boundaries shown in Fig. 11.8. Deissler [4] and coworkers place the buffer layer at a of 5 to 26, and Schlichting arid coworkers place it at a of 5 to about 70. Furthermore, current work seems to indicate that the location of the edge of these layers is not fixed in place but fluctuates up and down so these values indicate only the mean locations of these edges [5]. Thus, Fig. 11.8 may be too simple a picture of the actual behavior. Nonetheless, it provides a reasonable conceptual model and is able to correlate most of the available data with reasonable accuracy.

The value of E depends upon the values of the elonents in the stress and strain tensors. Under plane stress conditions, one of die principal stresses is zero and E is equal to Young s modulus, E. However, under plane strain conditions, the strain in one of the principal axes is zero and E = E/(l — v ) where v is Poisson s ratio. For most polymers 0.3 < v < 0.5 and the values of both Gic and Kic invariably are much greater when measured in plane stress. For the purposes both of toughness comparisons and component design, die plane strain values of Gic and Kic are preferred because th are the minimum values fm any given material. In order to achieve plane strain conditions, the following criteria need to be satisfied ... 

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