Longitudinal Tensile Loading of a Unidirectional Continuous Fiber Lamina

MECHANICS OF A UNIDIRECTIONAL PLY

Valery V. Vasiliev , Evgeny V. Morozov , in Advanced Mechanics of Composite Materials (Second Edition), 2007

3.4.1 Longitudinal tension

Stiffness and strength of unidirectional composites under longitudinal tension are determined by the fibers. As follows from Fig. 3.35, material stiffness linearly increases with increase in the fiber volume fraction. The same law following from Eq. (3.75) is valid for the material strength. If the fiber's ultimate elongation, ${\overline{\epsilon }}_{\text{f}}$ , is less than that of the matrix (which is normally the case), the longitudinal tensile strength is determined as

(3.104) ${\overline{\sigma }}_1^{+}=(E_{\text{f}}{v}_{\text{f}}+E_{\text{m}}{v}_{\text{m}}){\overline{\epsilon }}_{\text{f}}$

However, in contrast to Eq. (3.76) for E ₁, this equation is not valid for very small and very high fiber volume fractions. The dependence of ${\overline{\sigma }}_1^{+}$ on v _f is shown in Fig. 3.44. For very low v _f, the fibers do not restrain the matrix deformation. Being stretched by the matrix, the fibers fail because their ultimate elongation is less than that of the matrix and the induced stress concentration in the matrix can reduce material strength below the strength of the matrix (point B). Line BC in Fig. 3.44 corresponds to Eq. (3.104). At point C, the amount of the matrix reduces below the level necessary for a monolithic material, and the material strength at point D approximately corresponds to the strength of a dry bundle of fibers, which is less than the strength of a composite bundle of fibers bound with the matrix (see Table 3.3).

Fig. 3.44. Dependence of normalized longitudinal strength on fiber volume fraction (ˆ – experimental results).

Strength and stiffness under longitudinal tension are determined using unidirectional strips or rings. The strips are cut out of unidirectionally reinforced plates, and their ends are made thicker (usually glass–epoxy tabs are bonded onto the ends) to avoid specimen failure in the grips of the testing machine (Jones, 1999; Lagace, 1985). Rings are cut out of a circumferentially wound cylinder or wound individually on a special mandrel, as shown in Fig. 3.45. The strips are tested using traditional approaches, whereas the rings should be loaded with internal pressure. There exist several methods to apply the pressure (Tarnopol'skii and Kincis, 1985), the simplest of which involves the use of mechanical fixtures with various numbers of sectors as in Figs. 3.46 and 3.47. The failure mode is shown in Fig. 3.48. Longitudinal tension yields the following mechanical properties of the material

Fig. 3.45. A mandrel for test rings.

Fig. 3.46. Two-, four-, and eight-sector test fixtures for composite rings.

Fig. 3.47. A composite ring on a eight-sector test fixture.

Fig. 3.48. Failure modes of unidirectional rings.

•

longitudinal modulus, E ₁,

•

longitudinal tensile strength, ${\overline{\sigma }}_1^{+}$ ,

•

Poisson's ratio, v ₂₁.

Typical values of these characteristics for composites with various fibers and matrices are listed in Table 3.5. It follows from Figs. 3.40–3.43, that the stress–strain diagrams are linear practically up to failure.

Read full chapter

URL:

https://www.sciencedirect.com/science/article/pii/B9780080453729500038

Mechanics of a Unidirectional Ply

Valery V. Vasiliev , Evgeny V. Morozov , in Advanced Mechanics of Composite Materials and Structures (Fourth Edition), 2018

1.4.1 Longitudinal Tension

The stiffness and strength of unidirectional composites under longitudinal tension are determined by the fibers. As follows from Fig. 1.35, material stiffness linearly increases with increase in the fiber volume fraction. The same law following from Eq. (1.75) is valid for the material strength. If the fiber's ultimate elongation, ${\overline{\epsilon }}_f$ , is less than that of the matrix (which is normally the case), the longitudinal tensile strength is determined as

(1.104) ${\overline{\sigma }}_1^{+}=(E_f{v}_f+E_m{v}_m){\overline{\epsilon }}_f$

However, in contrast to Eq. (1.76) for $E_1$ , this equation is not valid for very small and very high fiber volume fractions. The dependence of ${\overline{\sigma }}_1^{+}$ on $v_f$ is shown in Fig. 1.44. For very low $v_f$ , the fibers do not restrain the matrix deformation. Being stretched by the matrix, the fibers fail because their ultimate elongation is less than that of the matrix and the induced stress concentration in the matrix can reduce material strength below the strength of the matrix (point B). Line BC in Fig. 1.44 corresponds to Eq. (1.104). At point C, the amount of matrix reduces below the level necessary for a monolithic material, and the material strength at point D approximately corresponds to the strength of a dry bundle of fibers, which is less than the strength of a composite bundle of fibers bound with matrix (see Table 1.3).

Figure 1.44. Dependence of normalized longitudinal strength on fiber volume fraction (○—experimental results).

The strength and stiffness under longitudinal tension are determined using unidirectional strips or rings. The strips are cut out of unidirectionally reinforced plates, and their ends are made thicker (usually glass–epoxy tabs are bonded onto the ends) to avoid specimen failure in the grips of the testing machine (Jones, 1999; Lagace, 1985). Rings are cut out of a circumferentially wound cylinder or wound individually on a special mandrel, as shown in Fig. 1.45. The strips are tested using traditional approaches, whereas the rings should be loaded with internal pressure. There exist several methods to apply the pressure (Tarnopol'skii & Kincis, 1985), the simplest of which involves the use of mechanical fixtures with various numbers of sectors as in Figs. 1.46 and 1.47. The failure mode is shown in Fig. 1.48. Longitudinal tension yields the following mechanical properties of the material:

Figure 1.45. A mandrel for test rings.

Figure 1.46. Two-, four-, and eight-sector test fixtures for composite rings.

Figure 1.47. A composite ring on an eight-sector test fixture.

Figure 1.48. Failure modes of unidirectional rings.

•

Longitudinal modulus, $E_1$

•

Longitudinal tensile strength, ${\overline{\sigma }}_1^{+}$

•

Poisson's ratio, ${\nu }_{21}$

Typical values of these characteristics for composites with various fibers and matrices are listed in Table 1.5. It follows from Figs. 1.40–1.43 that the stress–strain diagrams are linear practically up to failure.

Read full chapter

URL:

https://www.sciencedirect.com/science/article/pii/B9780081022092000013

Elastic Behavior of Materials: Continuum Aspects

A.M. Korsunsky , in Encyclopedia of Materials: Science and Technology, 2001

6.1 Uniaxial Tension

A slender rod subjected to longitudinal tension develops uniform strains ϵ _ij , and uniform stresses σ _ij . Any section transmits axial stress alone, σ₁₁, while all other stress components are equal to zero. This state of stress is called uniaxial tension. From Equation (16), the axial elongation ϵ₁₁ is found as

(17) $\begin{array}{l}{\epsilon }_{11}={\sigma }_{11}\frac{(\lambda +\mu )}{\mu (3\lambda +2\mu )}=\frac{{\sigma }_{11}}{E},\hfill \\ E=\frac{\mu (3\lambda +2\mu )}{(\lambda +\mu )}\hfill \end{array}$

The coefficient E is called Young's modulus. The ratio of transverse contraction experienced by the rod to axial elongation is called Poisson's ratio, and is given by

(18) $\nu =-\frac{{\epsilon }_{22}}{{\epsilon }_{11}}=\frac{\lambda }{2(\lambda +\mu )}$

Read full chapter

URL:

https://www.sciencedirect.com/science/article/pii/B0080431526004253

Elastic and Inelastic Deformation and Residual Stress

Alexander M. Korsunsky , in A Teaching Essay on Residual Stresses and Eigenstrains, 2017

2.9 Uniform Deformation

The simplest cases of deformation are observed when the strain tensor is uniform throughout the solid body.

Uniaxial tension . A slender rod subjected to longitudinal tension develops uniform strains ε _ij and uniform stresses σ _ij . Any section transmits axial stress alone, σ ₁₁, whereas all other stress components are equal to zero. This state of stress is called uniaxial tension. From Eq. (2.18), the axial elongation strain ε ₁₁ is found as

(2.19) ${\epsilon }_{11}={\sigma }_{11}\frac{\left(\lambda +\mu \right)}{\mu \left(3\lambda +2\mu \right)}=\frac{{\sigma }_{11}}{{\rm E}},E=\frac{\mu \left(3\lambda +2\mu \right)}{\left(\lambda +\mu \right)}\text{.}$

The coefficient E is called Young's modulus. The ratio of transverse contraction experienced by the rod to axial elongation is called Poisson's ratio and is given by

(2.20) $\nu =-\frac{{\epsilon }_{22}}{{\epsilon }_{11}}=\frac{\lambda }{2\left(\lambda +\mu \right)}\text{.}$

Equiaxial compression. Consider a body subjected to hydrostatic pressure P, σ _ij   =   −Pδ _ij . The bulk modulus K of an isotropic body is found as the ratio of P to the relative volume decrease, Δ   = ε _ii . Summing up Eq. (2.19) for i  = j  =   1…3:

(2.21) $\frac{{\sigma }_{11}+{\sigma }_{22}+{\sigma }_{33}}{3\left({\epsilon }_{11}+{\epsilon }_{22}+{\epsilon }_{33}\right)}=K=\lambda +\frac{2}{3}\mu =\frac{{\rm E}}{3\left(1-2\nu \right)}\text{.}$

Pure shear. Consider uniform pure shear ε ₁₂ (all other strain components are zero). The only nonzero stress component is

(2.22) ${\mathit{\sigma }}_{12}=2G{\mathit{\epsilon }}_{12}\text{.}$

The coefficient G is called the shear modulus, or modulus of rigidity,

(2.23) $G=\mu =\frac{E}{2\left(1+\nu \right)}\text{.}$

General uniform strain. In the general case of isotropic material subjected to uniform deformation, the principal stresses and strains are related as follows:

(2.24) ${\epsilon }_1=\frac{1}{E}\left[{\sigma }_1-\nu \left({\sigma }_2+{\sigma }_3\right)\right]\text{,}$

(2.25) ${\sigma }_1=\frac{E}{\left(1+\nu \right)\left(1-2\nu \right)}\left[\left(1-\nu \right){\epsilon }_1+\nu \left({\epsilon }_2+{\epsilon }_3\right)\right]\text{.}$

Read full chapter

URL:

https://www.sciencedirect.com/science/article/pii/B9780128109908000021

Fibre failure modelling

S. Pimenta , in Numerical Modelling of Failure in Advanced Composite Materials, 2015

8.3.3.3 Two-scales FE models

FE analyses have been extensively used to model the micromechanical response of composites under longitudinal tension ( Thionnet et al., 2014; Nedele and Wisnom, 1994; González and Llorca, 2006; Mishnaevsky and Brøndsted, 2009). However, a very fine mesh is required to accurately account for stress concentrations near fibre breaks, meaning that most FE models consider very small RVEs only. Nevertheless, Blassiau et al. (2009) and Thionnet et al. (2014) recently developed a coupled two-scales (micro–macro) FE model to predict the longitudinal failure process in UD composites, which is able to simulate composite specimens with millions of fibres.

The microscale FE analysis is deterministic and considers a 4   mm long UC with 32 linear-elastic isotropic fibres in a square arrangement, embedded in a visco-elastic matrix. Different damage states (with 2, 4, 8, 16 or 32 co-planar fibre breaks in the UC, uniformly dispersed in the cross section) were simulated, assuming a 35   μm fibre–matrix debond at each fibre break. The microscale model generates a library with the stiffness of the UC and stress concentrations in fibres neighbouring the break for the different damage states.

The macroscale FE analysis modelled each UC with one integration point and five realisations of single-fibre strength (assumed to follow a Weibull distribution scaled to the UC length according to Equation 8.2). This, combined with the stress concentrations calculated in the microscale model, allows the number of broken fibres at each integration point to evolve from an undamaged state to sequential damage states with 2, 4, 8, 16 and 32 broken fibres. The longitudinal stiffness associated with each integration point was degraded to the corresponding value calculated by the microscale model.

Failure was assumed to occur at the onset of a numerical instability, characterised by a rapid increase in remote strain under nearly constant remote stress; the critical damage state (after which failure is catastrophic) in a UD composite corresponds to the formation of clusters with 32 broken fibres (Thionnet et al., 2014). This model has been used to predict longitudinal tensile failure in UD composites, in laminates and in pressure vessels. Also, by considering a visco-elastic matrix, the model predicts that tensile strength should increase with higher strain rates (due to stiffening of the matrix), and that failure can occur under constant remote stress (due to relaxation of the matrix and progressive damage accumulation) (Thionnet et al., 2014); these predictions are qualitatively supported by experiments.

Read full chapter

URL:

https://www.sciencedirect.com/science/article/pii/B9780081003329000086

Retrieval studies for medical biotextiles

C.R. Gajjar , ... R. Guidoin , in Biotextiles as Medical Implants, 2013

Tests for physical properties

Changes in the physical properties of the retrieved biotextile implant can suggest the in vivo behavior of the implant during its service life. The possible mode of failure can be determined by studying these changes.

Crimp extension

Crimp extension refers to the extent to which the graft or biotextile structure stretches under longitudinal tension. A specimen of known relaxed length is extended on a mechanical tester, such as an Instron Universal Tester, so as to remove most of the crimps by applying a standard constant load of 1.2  N. The amount of crimp extension is calculated from the difference between the extended and relaxed lengths and expressed as a percentage of the original relaxed length. ³⁶

Dilation

This measures the extent to which a tubular prosthesis dilates under static internal pressure using a dilation measurement system. A 10-cm long segment of tubular prosthesis is mounted over a tubular latex membrane and held between two connectors, one of which is fixed and supplies the internal air pressure, while the other is attached to a low-friction track to which a constant longitudinal tension of 113  g is applied. The outer diameter of the graft is scanned by a laser micrometer while increasing the internal air pressure from 0 to 340   mm Hg in 20   mm Hg increments and returning back to zero pressure. The changes in the diameter are recorded and plotted to give a smooth curved relationship. The average change in diameter at 120   mm Hg is taken to be the dilation under normal physiological conditions. ³⁶

Bursting strength

The bursting strength gives the strength of the prosthesis wall. The standard procedure to measure the bursting strength of a vascular prosthesis, for example, can be found in ISO 7198. ³⁶ Any loss of strength over the time while the device is implanted in the body can be confirmed by a reduction in bursting strength of an explanted device compared to its unused control. Bursting strength measurements determined at different time intervals can be used to predict the long-term in vivo biostability performance of a biotextile implant. ⁹

Suture retention strength

Suture retention strength is given by the force required to pull a suture out of the prosthesis. The maximum force required (N) to pull the suture from the graft is measured using a mechanical tensile tester. The tests are generally conducted at 0° (parallel), 45° and 90° (perpendicular) to the longitudinal axis of the prosthesis to represent the different types of surgical end-to-end and end-to-side anastomoses that may be used to attach the device in vivo. The size and type of suture material may influence the results, so these variables should be recorded and reported with the results. In our laboratory we have found the use of size 0 to 3–0 stainless steel sutures provides reliable data.

Water permeability

The number of milliliters of filtered or distilled water that pass through a 1   cm² area of material per minute under a pressure head of 120   mm Hg is defined as the water permeability of the material. ³⁷ The measurement of water permeability (or porosity) is carried out according to the method described in ISO 7198. ³⁶ This gives an index of the interstitial leakage rate of the prosthesis, and if the rate is high enough, it indicates that the prosthesis needs to be coated or preclotted with the patient's whole blood prior to implantation so as to avoid excessive blood loss and hemorrhage. Note that some surgeons use the word 'porosity' incorrectly to refer to the water permeability of a prosthesis. These two terms have different technical meanings and should not be confused. ³⁷

Read full chapter

URL:

https://www.sciencedirect.com/science/article/pii/B9781845694395500089

Fiber Reinforcements and General Theory of Composites

L.J. HART-SMITH , in Comprehensive Composite Materials, 2000

1.21.2.1 Tension and Compression Failures of Fibers Expressed at the Lamina Level

The first failure mode to be discussed is that of the fibers. The measured reference strengths are for longitudinal tension or longitudinal compression of uniaxial composite laminae. That is, it is the load carried by the fibers and the resin, when the fibers fail, normalized with respect to the cross-section of the lamina, not of the fibers. Only two such measurements are possible, even though there are more than two potential failure modes. Under axial compression, if the fibers are thin enough, as with the newer IM-6 high-strain carbon fibers, failure will be by some form of instability—kink bands or buckling because the matrix is not stiff enough to support the fibers which may themselves be misaligned. Since the reference uniaxial strength is measured, rather than computed, the differences are immaterial, because the addition of direct transverse loads (tension or compression) will not affect the failing strength of the fibers, at least not for these modes of failure. At the fiber level, such a failure characteristic would appear as a constant longitudinal stress line. At the unidirectional lamina level, the same characteristic, allowing for different transverse properties of the fibers and resin, appears far closer to a constant longitudinal strain line. The deviation is so small for carbon and glass fiber reinforced polymer composites that it is customary, and reasonable, to assume that this failure mechanism is covered by a constant strain line on the lamina strain plane. The same is true of fiber failures under tensile loads that are associated with brittle fracture at surface notches of glass fibers or inclusions in carbon fibers. The characterizations of these two possible failure modes are shown in Figure 2. They form the fiber-failure portion of the now classical maximum strain model for fiber–polymer composites, the appropriateness of which for what were then called advanced composites was first recognized in the 1960s (Waddoups, 1968). The same conclusion was reached independently for glass-fiber polymer composites (Puck and Schneider, 1969).

Figure 2. Longitudinal tension and compression failure loci on lamina strain plane.

It will suffice here to consider only membrane states of stress and strain in laminates, away from the edges. This enables us to equate the same in-plane strains in the laminate to each and every lamina of which it is composed. Bending effects are easily added, using well-established techniques (see, e.g., Jones, 1975). (Edge delaminations are also a specialist subject.)

The strength limits in Figure 2 can be expressed in an extremely simple mathematical form to facilitate application of this theory via computers. The longitudinal strength for uniaxial loads parallel to the fibers lies between the following bounds:

(1) ${{\epsilon }_{11}}^{\text{c}}⩽{\epsilon }_{11}⩽{{\epsilon }_{11}}^{\text{t}}$

in which e is the strain parallel to the fibers, 1 is the reference axis in the lamina for the fibers, and c and t denote compression and tension, respectively. These longitudinal strains are common between the fibers and resin matrix, and hence the lamina.

Read full chapter

URL:

https://www.sciencedirect.com/science/article/pii/B0080429939002187

Mechanical Behavior of Reinforcement

Zhenhai Guo , in Principles of Reinforced Concrete, 2014

6.4.2 Cold-drawn

When the reinforcement is stretched and passed through a die of hard metal, it is elongated and its diameter is reduced under common action of longitudinal tension and transverse compression, and its volume is decreased slightly. The original steel is normally wire rod of diameter 6 mm or 8 mm, its diameter is reduced by 0.5–2.0 mm after every cold-drawn, which is called cold-drawn wire of low-carbon steel.

Plastic deformation of the reinforcement occurs intensely and the crystalline grain in it is deformed and displaced considerably during the cold-drawing process, so its strength is greatly increased and the ultimate elongation is reduced correspondingly, and the stress–strain curve of it is similar to that of hard steel (Fig. 6-14). The cold-drawn wire is used widely in engineering practice in China to save steel used and to reduce the cost of the structure.

FIG. 6-14. Stress–strain curve of cold-drawn wire of low-carbon steel

The main mechanical behavior of the cold-drawn wire, including nominal yield strength (f _y ), ultimate strength (f _b ) and elongation (δ ₅ or δ ₁₀), and modulus of elasticity, depends mainly upon the kinds of original steel and the reducing rate of its section area (Fig. 6-15), but is not apparently influenced by the number of cold-drawing.

FIG. 6-15. Behavior of cold-drawn wire of low carbon steel [6-11]: (a) ultimate strength, (b) ultimate elongation (δ ₁₀)

According to the experimental data reported in China [6-11], the ultimate strength of cold-drawn wire of low-carbon steel reaches about 1.6–2.0 times that of original steel, and the ratios between the proportional limit and nominal yield strength with ultimate strength are respectively f _p /f _b = 0.71–0.84 and f _0.2/f _b = 0.9–1.0. However, the ultimate elongation of its diameter of 3–5 mm is only δ ₁₀ = 2.5–5.0%, i.e. 10–15% of that of the original steel, and the modulus of elasticity is decreased slightly.

The stress–strain relation of the cold-drawn wire of low-carbon steel is suggested in reference [6-12] as below:

(6-12) $\begin{array}{l}0\le {\epsilon }_s\le {\epsilon }_p{\sigma }_s=E_s{\epsilon }_s\\ {\epsilon }_s>{\epsilon }_p{\sigma }_s=1.075f_b-\frac{0.6}{{\epsilon }_s}\end{array}\},$

where the strain corresponding to proportional limit is ε _p = 2.5×10⁻³.

Read full chapter

URL:

https://www.sciencedirect.com/science/article/pii/B9780128008591000062

Steam boiler component loading, monitoring and life assessment

Taler J. , Duda P. , in Power Plant Life Management and Performance Improvement, 2011

12.3.4 Monitoring of temperature and stress distributions in pressure components

The following section presents temperature and stress transients for selected pressure elements from a steam power boiler with a capacity of 650×10³ kg/h, which produces steam with the following parameters: p =   13.5 MPa, T = 540 °C. The re-heated steam parameters are p = 2.2   MPa and T = 540 °C. From among many monitored construction elements, four were chosen for this analysis: the boiler drum and three headers (Table 12.1). Limit stresses σ _min and σ _max are determined using a fatigue strength diagram (EN 12952-3, 2001; TRD, 2002) under the assumption of n = 2000 start-ups from a cold state. Table 12.2 presents the results obtained from the calculation of the allowable heating and cooling rates of the elements determined from equations [12.2] to [12.6].

Table 12.1. Monitored pressure elements of a power boiler with 650 × 10³kg/h capacity

	r out (m)	r in (m)	α (m2/s)	φ w (MPa/K)	ß (1/K)	k (W/mK)	E (MPa)	c (J/kgK)	ύ (kg/m3)
Boiler drum (18GMNA) ϕ 1800×115	0.9	0.785	8.15×10−6	3.51	1.35×10−5	39	1.82 ×105	610	7840
Live steam outlet header (12H1MF) ϕ 377 × 50	0.1885	0.1385	8.52 ×10−6	3.76	1.33 ×10−5	41	1.98 ×105	625	7700
Live steam attemperator (III) of (12H1MF) ϕ 377×50	0.1885	0.1385	8.01 ×10−6	3.90	1.38 ×10−5	40	1.98 ×105	650	7680
Steam re-heater outlet header (15H1MF) ϕ 630×30	0.315	0.285	7.96 ×10−6	3.34	1.35 ×10−5	38	1.73 ×105	620	7700

Table 12.2. Calculated allowable stresses and heating and cooling rates of pressure elements using TRD regulations

	σmin(MPa)	σmax(MPa)	V T heating rate at beginning of start-up (K/min)	V T heating rate at the end of start-up (K/min)	V T cooling rate at beginning of shut-down (K/min)	V T cooling rate at the end of shut-down (K/min)
Boiler drum 18GMNA (15NcuMNb)	–198.567	511.310	2.468	6.355	–2.468	–6.355
Live steam outlet header 12H1MF	–192.275	312.295	9.448	15.346	–9.448	–15.346
Live steam attemperator (III) 12H1MF	–195.737	315.758	9.618	15.516	–9.618	–15.516
Steam re-heater outlet header 15H1MF	–234.615	295.373	46.945	59.102	–46.945	–59.102

For the study, 16 time periods of transient power boiler operation, which included start-up and shut-down operations, were recorded and analysed. Temperature and stress distributions in the horizontal elements, such as the boiler drum and outlet headers, were obtained on the basis of temperature readings taken at seven points, located on the outer insulated surface at a uniform distance from each other. The methods for determining transient temperature and stress distributions based on temperature measurements at the outer surface of the pressure component are presented in the following references: Duda (2003, 2005), Duda and Taler (2000), Duda et al. (2004), Taler (1999), Taler and Duda (2006), Taler and Zima (1999), Taler et al. (1999, 2002). It was assumed that a cylindrical element can lengthen and bend itself freely. Figure 12.9 shows the division of half of the cylindrical element's cross-section into finite elements. Temperature distribution and stresses in the component were determined based on the solution of the inverse heat conduction problem (IHCP).

12.9. Division of the half cross-section of the horizontal cylindrical element into finite elements; temperature is measured at points 1 to 7 (nodes 1, 4, 6, 8, 10, 12, 2).

The analysis of temperature and stress field results will be presented for the outlet header of the steam re-heater. The determined temperature and stress transients are shown in Figs 12.10 to 12.14. The measured temperature transients at points 1 and 7, i.e. at the lowest and highest points, and the pressure transient inside the header are presented in Fig. 12.10.

12.10. Measured pressure and temperature transients on the outer header's re-heater surface.

12.14. Equivalent stress transients on outlet head's inner surface at points located opposite points 1–7.

One can observe that while the wall temperature at the lower part of the outlet header is about 150 °C, the upper part has a considerably higher temperature. This is most probably caused by the flow of non-evaporated water from the re-heater's non-drainable pipe coils into the re-heater outlet header. Water accumulates in the lower part of the outlet header. The temperature transients at the seven points on the inner surface, located opposite the measurement points on the outer surface, are shown in Fig. 12.11. The temperature difference transient ΔT in the inner surface of the wall at the lowest and highest points ΔT = T _g – T _d is also presented.

12.11. Temperature transients on the outlet header's inner surface (opposite points 1–7) and temperature difference transients between the outlet header's top and bottom ΔT = T _g–T _d, T _g and T _d are the outlet header's inner surface temperature at the highest and lowest points respectively.

Owing to a relatively high temperature difference recorded on the header's circumference, axial thermal stresses are high (see Fig. 12.13). Therefore, longitudinal tension stresses occur in the header's lower, colder part. One should, therefore, expect a relatively high thermal stress on the hole edges of downcomers, because of a stress concentration on the hole edges. Pressure-induced maximal equivalent stresses in the header are not, as absolute values, much larger than axial thermal stresses, since the pressure of the re-heated steam is relatively low.

12.13. Axial thermal stress transients on the outlet header's inner surface at the points located opposite points 1–7.

Fig 12.12. Circumferential thermal stress transients on the outlet header's inner surface at the points located opposite points 1–7.

Read full chapter

URL:

https://www.sciencedirect.com/science/article/pii/B9781845697266500122

Application of modern aluminium alloys to aircraft

E.A. StarkeJr., J.T. Staley , in Fundamentals of Aluminium Metallurgy, 2011

24.3.1 Property requirements for fuselage

The fuselage is a semi-monocoque structure made up of skin to carry cabin pressure (tension) and shear loads, longitudinal stringers or longerons to carry the longitudinal tension and compression loads, circumferential frames to maintain the fuselage shape and redistribute loads into the skin, and bulkheads to carry concentrated loads. In high-performance military aircraft, thick bulkheads are used rather than frames. The fuselage can be divided into three areas: crown, sides and bottom. Predominant loads during flight are tension in the crown, shear in the sides and compression in the bottom. These loads are caused by bending of the fuselage due to loading of the wings during flight and by cabin pressure. Taxiing causes compression in the top and tension in the bottom, however these stresses are less than the in-flight stresses. Strength, Young's modulus, fatigue initiation, fatigue crack growth, fracture toughness and corrosion are all important, but fracture toughness is often the limiting design consideration.

Read full chapter

URL:

https://www.sciencedirect.com/science/article/pii/B9781845696542500249

crumewair1937.blogspot.com

Source: https://www.sciencedirect.com/topics/engineering/longitudinal-tension

Share this post