Yasushi Takase

Stress concentration factors for round and flat test specimens with notches

Abstract The stress concentration problem of round and flat bars with V-shaped notches under various loadings is especially important for test specimens used to investigate the fatigue strength of materials. Accurate stress concentration factors have been given in a recent analysis of the body force method. However, the results of the solutions have been presented in tabular form, which is not suitable for engineering applications. In this paper convenient formulae, which give the stress concentration factors with better than 1% accuracy, are proposed using the Neuber formula and the solution of a V-shaped notch in a semi-infinite plate. The stress concentration factors are also provided in a graphical way on the basis of the formulae.

Generalized stress intensity factors of V-shaped notch in a round bar under torsion, tension, and bending

Abstract In this study, generalized stress intensity factors K I, λ 1 , K II, λ 2 , and K III, λ 4 are calculated for a V-shaped notched round bar under tension, bending, and torsion using the singular integral equation of the body force method. The body force method is used to formulate the problem as a system of singular integral equations, where the unknown functions are the densities of body forces distributed in an infinite body. In order to analyze the problem accurately, the unknown functions are expressed as piecewise smooth functions using three types of fundamental densities and power series, where the fundamental densities are chosen to represent the symmetric stress singularity and the skew-symmetric stress singularity. Generalized stress intensity factors at the notch tip are systematically calculated for various shapes of V-shaped notches. Normalized stress intensity factors are given by using limiting solutions; they are almost determined by notch depth alone, and almost independent of other geometrical parameters. The accuracy of Benthem–Koiter’s formula proposed for a circumferential crack is also examined through the comparison with the present analysis.

Stress concentration factors for shoulder fillets in round and flat bars under various loads

Abstract The stress concentration problem of shoulder fillets in round and flat bars under various loads is often encountered in machine design of shafts. Also it is important for test specimens used to investigate the mechanical properties of materials. Accurate stress concentration factors (SCFs) have been given in a recent analysis of the body force method. However, the results of the solutions have been presented in tabular form which is not suitable for engineering applications. For notched bars, Neuber proposed the simple approximate formula K tN which is useful for a wide range of notch shape: 1/( K tN − 1) m = 1/( K ts − 1) m + 1/( K td − 1) m and m = 2. Here, K ts and K td are exact solutions for shallow and deep notches, respectively. Neubers simple formula has been used for >40 years in the design of notched bars because of its convenience. In this study, similar convenient equations K tN are initially proposed as an extension of Neubers formula to the problem of shoulder fillet. In this formula new definitions of K ts and K id are used corresponding to two extreme cases of shoulder fillet in round and flat bars. Next, the most suitable exponent m is determined so as to minimize the difference between K tN and accurate K t , that is, the results of the body force method. Next, by applying the least squares method to the ratio K t / K tN more accurate formulas are proposed. The formulas proposed in this paper are found to give the stress concentration factors with better than 1 % accuracy. In addition, the stress concentration factors are also provided in a graphical way on the basis of the formula so they can be used easily in design or research.

Generalized stress intensity factors in the interaction between two fibers in matrix

To evaluate the mechanical strength of fiber reinforced composites it is necessary to consider singular stresses at the end of fibers because they cause crack initiation, propagation, and final failure. The singular stress is expressed by generalized stress intensity factors defined at the corner of fibers. As a 2D model an interaction between rectangular inclusions under longitudinal tension is treated in this paper. The body force method is used to formulate the problem as a system of singular integral equations with Cauchy-type or logarithmic-type singularities, where the unknown functions are the densities of body forces distributed in infinite plates having the same elastic constants as those of the matrix and inclusions. In order to analyze the problem accurately, the unknown functions are expressed as piecewize smooth functions using two types of fundamental densities and power series, where the fundamental densities are chosen to represent the symmetric stress singularity of 1/r1−λ1 and the skew-symmetric stress singularity of 1/r1−λ2. Then, generalized stress intensity factors at the end of inclusions are systematically calculated for various locations, spacings and elastic modulus of two rectangular inclusions in a plate subjected to longitudinal tension.

Fatigue strength of notched specimens having nearly equal sizes of ferrite

Abstract In this study, rotating bending fatigue tests were conducted on circumferential notched large and small specimens of three kinds of carbon steel with nearly equal (20 μm) ferrite grain sizes but different volume fractions of pearlite. The effect of microstructures on the fatigue strengths σws (the limit stress for slip bands), σw1 (the limit stress for macrocrack initiation), and σw2 (the limit stress for fracture) is discussed by comparing these values in three kinds of carbon steel. The main results newly obtained are as follows. (1) Since σws is localized to a highly specified region, variation of Ktσws (maximum stress repeated at the notch root in the limit stress for slip bands) is small, irrespective of notch root radius. (2) If the grain size of ferrite is nearly equal, variation of σw1 is small irrespective of pearlite under the threshold amount of pearlite. The threshold volume fraction of pearlite is about 50%. (3) In medium-carbon steel, σw2 increases with increasing grain size of ferrite. (4) Notch root radius at the branch point, ϱ0, varies depending on the grain size of ferrite. (5) The values of Ktσw1 (maximum stress repeated at the notch root in the limit stress for macrocrack initiation) and Ktσw2 (maximum stress repeated at the notch root in the limit stress for fracture) can be determined by the notch root radius ϱ alone, independent of geometrical conditions.

Interaction between fillet and crack in round and flat test specimens

Abstract In this paper, the stress concentration problem of a fillet in round and flat test specimens under tension is analyzed by the body force method. The stress field induced by a ring force acting in the radial and axial directions in an infinite body, and a point force in a semi-infinite plate are used as fundamental solutions to solve these problems. The stress concentration factors of a fillet in a stepped round bar and a stepped flat bar are systematically calculated under various geometrical conditions. Through comparison of the present results with previous research, it is found that Petersons stress concentration charts based on photoelastic tests give underestimated stress concentration factors by about 13% for the worst cases. The stress distribution at the narrow section of the test specimen without a crack is investigated and the stress intensity factor of the test specimen with a fillet and a crack is systematically calculated. As a result, the geometrical condition that the interaction between the fillet and crack disappears is discussed.

Strength Analysis for Shrink Fitting System Used for Ceramics Rolls in the Continuous Pickling Line

Cast iron and steel rolls used in the continuous pickling line must be changed frequently because the continuous acid wash equipment induces wear on the roll surface in a short period. The damage portions are usually repaired by using the flame spray coating. Recently, ceramics materials are planed to be introduced to prevent the damage because of their high abrasion and corrosion resistances. In this study new roll structure is considered where a ceramics sleeve is connected with steel shafts at both ends by shrink fitting. Here, the ceramics sleeve may provide a longer lifetime and reduces the cost for the maintenance. However, attention should be paid to the maximum tensile stresses appearing between the ceramics sleeve, spacer rings and steel shafts because the fracture toughness, plasticity and fatigue strengths of ceramics are extremely lower than the values of steel. In this study, finite element method analysis is applied to the new structure, and the maximum tensile stress and stress amplitude have been investigated with varying the dimensions of the structure. Fatigue strengths of ceramics are also considered under several geometrical conditions.

Formula Of Stress Concentration Factors For RoundAnd Flat Bars With Notches

Stress concentration of V-shaped notches in round and flat bars under various loading is important especially for the test specimen used to investigate the mechanical properties of materials. For notched bars, Neuber proposed simple approximate formula K^ useful for wide range of notch shape: 1/(K^ -1)™ = l/(Kfe -1)™ +l/(K|d -1) and m=2. Here, K% and K%, are exact solutions for shallow and deep notches, respectively. In this study, first, most suitable exponent m is determined so as to minimize the difference between K^ and accurate K,, that is, the results of body force method. Next, by applying the least squares method to the ratio K/K^ more accurate formulae are proposed. The formulae proposed in this paper are found to give the stress concentration factors with better than \% accuracy.

Strain Rate Concentration Factor for Round and Flat Test Specimens

In this study, the strain rate concentration is considered for high speed tensile test, which is now being recognized as a standard testing method. To evaluate the impact strength of engineering materials, Izod and Charpy tests are unsuitable since they cannot control the impact speeds and therefore the testing results do not coincide with the real failure of real products. For smooth specimens, the strain rate can be determined from the tensile speed \( u/t \) and specimen length \( l \) as \( \dot{\varepsilon }_{smooth} = u/tl \). For notched specimens, however, the strain rate at the notch root \( \dot{\varepsilon }_{notch} \) should be analyzed accurately. In this study, therefore, the strain rate concentration factor defined as \( K_{{t\dot{\varepsilon }}} = \dot{\varepsilon }_{notch} /\dot{\varepsilon }_{smooth} \) is studied with varying the notch geometry and specimen length for round and flat test specimens.

Intensity of singular stress fields of wedge-shaped defect in human tooth due to occlusal force before and after restoration with composite resins

Wedge-shaped defects are frequently observed on the cervical region of the human tooth. Previously, most studies explained that improper tooth-brushing causes such defects. However, recent clinical observation suggested that the repeated stress due to occlusal force may induce the formation of these wedge-shaped defects. In this study, therefore, two-dimensional human tooth models are considered with and without a wedge-shaped defect by applying the finite element method. To evaluate large stress concentrations accurately, a method of analysis is discussed in terms of the intensity of singular stress fields appearing at the tip of the sharp wedge-shaped defect. The effects of the position and direction of occlusion on the intensity of singular stress fields are discussed before and after restoration with composite resins.