Notch stress concentration factor

Figure 4.20 Values of stress concentration factor, Kt, as a function of radius, r, with 3a limits for a circumferentially notched round bar in tension [d A/(0.5, 0.00266) inches, = 0.00333 inches] (adapted from Haugen, 1980)...

For the purposes of performing an impact test on a material it is proposed to use an elastic stress concentration factor of 3.5. If the notch tip radius is to be 0.25 mm estimate a suitable notch depth. 

Fracture is caused by higher stresses around flaws or cracks than in the surrounding material. However, fracture mechanics is much more than the study of stress concentration factors. Such factors are useful in determining the influence of relatively large holes in bodies (see Section 6.3, Holes in Laminates), but are not particularly helpful when the body has sharp notches or crack-like flaws. For composite materials, fracture has a new dimension as opposed to homogeneous isotropic materials because of the presence of two or more constituents. Fracture can be a fracture of the individual constituents or a separation of the interface between the constituents. 

Layup Young s modulus (GPa) Measured stress concentration factor Predicted stress concentration factor Notched strength, [Pg.344]

In the blends, the maximum stress at low rates decreases, as expected, with increasing rubber concentration. At high rates, the 15 and 20% blends show an unexpectedly strong upswing in the maximum stress. The maximum stress before fracture can increase if the stress-concentration factor ahead of the notch is lowered. 

It is worthwhile to consider whether the classical theories (or criteria) of failure can still be applied if the stress (or strain) concentration effects of geometric discontinuities (eg., notches and cracks) are properly taken into account. In other words, one might define a (theoretical) stress concentration factor, for example, to account for the elevation of local stress by the geometric discontinuity in a material and still make use of the maximum principal stress criterion to predict its strength, or load-carrying capability. 

The parenthetical term is the theoretical stress concentration factor for the notch. By squaring a/b and recognizing that b /a is the radius of curvature p, Om may be rewritten as follows ... 

Stress raisers such as steps and notches are taken into account by using a further factor, k, calculated from the stress concentration factor (k,) and the material notch sensitivity q as follows ... 

All of the alloys were tested at room temperature, —112, and —320°F with Smooth specimens and notched specimens of the design showm in Fig. 1 (theoretical stress concentration factor [ ] Kt 17) certain of the alloys were also tested at —423°F with similar specimens. At room temperature, both longitudinal and transverse specimens were tested at the other temperatures, testing was limited to transverse specimens. 

From the data in Fig. 6, it is apparent that there are no marked changes in the relative ratings of these alloys dependent upon the notch tip radius within the range from 0.001 to 0,009 in, representing theoretical stress concentration factors from 6 to 17. The X7106 1.41--------------------------1-------r... 

Nominal notch length, in. Net failure stress, iCP lb./in. Stress concentration factor K % initial Strength retained ... 

Tj =2PI TTd). As a final example, consider a single edge notch in a plate under uniaxial tension, as shown in Fig. 8.28. The ordinate of this graph will be equivalent to /[crV(OT)] in the limit of p=0 (/f, is the stress concentration factor, a22 l[Pg.234]

Figure 8.28 Stress concentration factor as a function of notch radius for a single edge-notched beam. (Adapted from Rooke et al., 1981, reproduced courtesy of Elsevier Science Ltd, Kidlington, UK.)...

The report of the inquiry [111] criticised the design and fabrication of the alterations made to the original pontoon. The actual cause of the accident was the failure of some tie bars in the detail around the jacking points. The failure was due to brittle fracture which initiated from severe notches such as a small radius curve at the fillet between the spade end and the shank of the tie bar. Weld defects and fatigue cracks were also present in tie bars subsequently recovered from the sea bed. The tie bars had been flame cut to shape and had weld repairs visible to the eye. There had been no post welding heat treatment of the steel. The steel complied with the original specification but tests showed low Charpy V notch impact values. Photo elastic tests indicated a stress concentration factor of 7 at the fillet between the spade end and the shank. The fracture was initiated in the opinion of the inquiry tribunal by the low ambient temperature of around 3°C. 

The deteriorating effects of cracks and notches on material properties are represented by the stress concentration factor... 

Question by R. Agricola, The Martin Company In the curves relating notch properties, there was no mention of the values used. Could you clarify the stress concentration factor used ... 

Answer by author The stress concentration factor for the notch-tensile specimens was between 4.4 and 4.5. 

Many investigations have been made on the low-temperature properties of aluminum alloys [1-4] however, in addition to the determination of tensile and elastic properties as a function of temperature, notched tensile properties and notched/unnotched tensile ratios were determined. The notched/unnotched ratios were determined as a function of temperature in order to evaluate the toughness, which is often referred to in terms of resistance to brittle fracture, or notch sensitivity [5-7]. A notched specimen with a stress concentration factor K oi 6.3 was selected for use in this investigation because previous axial fatigue tests of complex welded joints, and fatigue and burst tests of pressure vessels made of 301 extra full hard stainless steel exhibited excellent correlation with notched/unnotched tensile ratios obtained with this value of over a range of temperatures... 

The aluminum alloys used in this investigation and their history and chemical analyses are listed in Table I. The materials were tested in the "as-received" condition without further heat treatment or working. The tensile specimens used in this investigation are shown in Fig. 1. All tensile specimens were inspected and individually measured for area determination. Notched specimens were inspected and measured by means of an optical comparator and all specimens out of tolerance were rejected. The stress concentration factor, as determined by [(V2 width between notches)/(radius of the notch) s 6.3 with tolerance limits of 5.7 to 7.1. 

Stress Concentrators and Stress Concentration Factor. Just as all materials, polymer-based materials exhibit structure imperfections of various kinds. They appear already in processing, during handling in transport, as well as in service. Because of the presence of crazes, scratches, cracks, and other imperfections, mechanical properties of real polymeric materials are not as good as they theoretically could be. In this section we deal particularly with stress concentrators such as cracks (which appear although we did not want them) and notches (which are made on purpose to have well-defined cracks). 

The Type le specimen is designed to incorporate the best attributes of all of the other specimens. The Type le has the same a notch acuity or stress concentration factor as the Typie Id specimen, which is the highest of all of the other specimens (Iq = 4.1 v 3.1), and therefore is considered to be... 

Using the linear stress assumption the maximum stress at the root of the notch is the product of the nominal stress and the stress concentration factor a]j. Calculations of for general shapes of notch are available in the literature, but when the crack length c is much greater than the notch tip radius p, ak reduces to the simple expression ak = 2 Jcjp. 

The critical values of the stress concentration factor Kj were calculated from the classic formula of LEFM for the initiation of crack propagation at the notch tip and corresponding values of load were taken into account. 

Both Eqs. (11.1) and (11.2) account for the effect of transverse strain on plastic strain intensity factor characterized by the modified Poisson s ratio, V. In Eq. (11.1), this is accounted for by the ratio Sy/Sa, whereas in Eq. (11.2) the ratio Eg/E serves the same purpose as will be shown later. The modified Poisson s ratio in each case is intended to account for the different transverse contraction in the elastic-plastic condition as compared to the assumed elastic condition. Therefore this effect is primarily associated with the differences in variation in volume without any consideration given to the nonlinear stress-strain relationship in plasticity. Instead the approaches are based on an equation analogous to Hooke s law as obtained by Nadai. Gonyea uses expression (rule) due to Neuber to estimate the strain concentration effects through a correction factor, K, for various notches (characterized by the elastic stress concentration factor, Kj). Moulin and Roche obtain the same factor for a biaxial situation involving thermal shock problem and present a design curve for K, for alloy steels as a function of equivalent strain range. Similar results were obtained by Houtman for thermal shock in plates and cylinders and for cylinders fixed to a wall, which were discussed by Nickell. The problem of Poisson s effect in plasticity has been discussed in detail by Severud. Hubei... 

To design notched components, knowledge of Ki is required. Therefore, empirical formulae have been determined that can be used to calculate for different geometries and load cases. They are collected in tables e. g., Peterson s Stress Concentration Factors [109] or Dubbel [18]. One example, a shaft with a circumferential notch under tensile load, is shown in figure 4.3. The dimensions in the figure are the outer diameter D, the diameter at the notch root d, the notch depth t (with 2t = D — d), and the notch radius q. 

Fig. 4.3. Diagram of the stress concentration factor K% of a shaft with a circumferential notch under tensile loading (after 18 ). From the lines in the diagram, the line with the appropriate ratio g/t has to be selected. Next, the intersection with...

In the previous section, we defined the stress concentration factor Kt (equation (4.1)) for linear-elastic materials. As the example at the end of the previous section shows, it cannot be used directly for the case of ductile materials, for yielding at the notch root reduces the stresses. In this section, we discuss how the influence of a notch can be taken into account even in ductile materials. 

Fig. 4.5. Qualitative dependence of the stress concentration factors on the load. Sp is the strain at yielding (stress Rp) in the notch root...

For very small notch radii, the calculation of the stress concentration factor is problematic and the methods of fracture mechanics are more precise. Nevertheless, the fact that there is a singularity at the crack tip is reflected correctly by K. ... 

As explained in chapter 4, notches cause a stress concentration in a component. Thus, it should be expected that notches also affect the fatigue strength of a component. The stress concentration at the notch root is again described by the stress concentration factor Kt according to equation (4.1) ... 

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