A Continuous Carbon Fiberepoxy Composite is Required to

Analyzing surface quality in machined composites

K. Palanikumar , in Machining Technology for Composite Materials, 2012

6.4.2 Carbon fiber reinforced polymer (CFRP) composites

Carbon fiber reinforced polymer (CFRP) composite materials are finding increased applications in many areas. They are strong and light, and have usage in aerospace as well as in sail boats, and notably in modern bicycles and motor cycles, where high strength-to-weight ratios are required. They are also used in laptops, tripods, fishing rods, racquet frames, stringed instrument bodies and golf clubs (Palanikumar, 2010). Process variables may be varied to vary stiffness and strength of the carbon fibers and they are available in high modulus and intermediate modulus forms. Since the high material damping of carbon fiber–epoxy composite materials can dissipate any vibration of the composite structure that is induced, they are used for manufacturing high-speed transmission shafts (Reugg and Habermeir, 1980), machine-tool spindles (Lee et al., 1985), and robot arms (Lee et al., 1991). If carbon fiber–epoxy composites are used in robot arms or machine elements, accurate machining of the materials by processes such as turning, milling and drilling are required to provide bearing-mounting and adhesive-joining surfaces. Machining of carbon fiber–epoxy composite materials is not the same as machining conventional plain metals. The wear of sintered-carbide tools and high-speed steel tools is very severe. Hence, the cutting speed and feed rate of the machining operation should be selected carefully in the machining of carbon fiber–epoxy composites (Ki Soo Kim et al., 1992). Also, surface damage such as cracking and delamination of the machined surfaces is severe and obtaining a low surface-roughness is not easy (Lubin, 1982).

For some machining experiments (Palanikumar, 2010), carbon fiber in the form of roving was dipped into a catalyzed polyester resin and filament wound with an orientation angle of ±   45° to produce a cylindrical CFRP tube. After curing and removal from the mandrel. The cutting tool used for the machining was a cemented carbide type (TPGN 16 03 04 H13A) and its geometry was with the rake angle of 6°, a clearance angle of 11°, an edge major tool cutting angle of 91°, and a cutting edge inclination angle of 0°. A tool holder having the specification PCLNR 1616   K12 was used. The work material and cutting tool with tool holder used in the investigation is presented in Fig. 6.17.

Figure 6.17. (a) CFRP tube and (b) cutting tool used for the experiments.

The influence of surface characteristics in the machining of CFRP composites is assessed by conducting machinability tests. A typical surface profile observed in turning of CFRP composites is presented in Fig. 6.18. The figure represents a schematic of the surface profile obtained when measuring surface roughness on the machined material, and it represents a roughness value of 1.32 μm. The nature of the surface after machining is clearly seen from the picture.

Figure 6.18. Typical surface roughness profile observed in machining of CFRP composites.

The variation of surface roughness with respect to the cutting speed for a varying feed rate at a constant depth of cut is presented in Fig. 6.19. The figure indicates that an increase of cutting speed slightly reduces the surface roughness in the machining of CFRP composites. At high feed rates, no definite trend is seen. An increase of spindle speed slightly increases the surface roughness and then reduces it. The results indicate that an increase or decrease of cutting speed does not show any variation in the surface roughness. When the material is cut at a low cutting speed, the cutting is carried out by the plowing effect of the tool, which results in a perfect shearing of the fibers, which results in a good surface finish; hence, there is no definite cutting speed recommented for the machining of CFRP composites, but a medium speed is best. An increase of the feed rate increases the surface roughness in machining of CFRP composites. This increase increases the load on the tool and increases the cutting force generated during turning, which in turn increases the surface roughness.

Figure 6.19. Variation of the arithmetic average surface roughness (R _a) with cutting speed for varying feed rates (depth of cut   =   1.0   mm).

The variation of surface roughness with cutting speed at varying depths of cut is presented in Fig. 6.20. The figure indicates that an increase in depth of cut increases the surface roughness in the turning of CFRP composites. The increase in the depth of cut increases the width of the cut and the forces on the cutting tool, which in turn produces a rough surface. Increase in the depth of cut also increases the contact between the tool and the workpiece, which leads to a rougher surface. The variation of surface roughness with feed rate for varying depths of cut is presented in Fig. 6.21. The figure indicates that an increase of feed and depth of cut increases the surface roughness in machining of CFRP composites. Among the parameters studied, feed rate is the main parameter that influences the surface roughness in turning of CFRP composites, whereas the cutting speed has only little effect. Figure 6.22 shows a micrograph of the turned surfaces at different feed rates by keeping the cutting speed and depth of cut at a constant medium level.

Figure 6.20. Variation of the arithmetic average surface roughness (R _a) with cutting speed for varying depth of cut (feed rate   =   0.15   mm/rev).

Figure 6.21. Variation of the arithmetic average surface roughness (R _a) with feed for varying depth of cut (feed   =   0.15   mm/rev).

Figure 6.22. SEM micrographs of machined surfaces in machining CFRP composites: (a) surface observed at low feed rate; (b) surface observed at medium feed rate; (c) surface observed at high feed rate.

Figure 6.22a shows the surface profile observed at a low feed rate. This figure indicates the comparatively better surface. In Fig. 6.18, the white spot shows the machined resin that is used for the fabrication of composites. Figure 6.22b shows the surface profile observed in the machining of CFRP composites at a medium feed rate. The figure shows the feed marks on the specimen. Figure 6.22c shows the surface profile observed at a high feed rate. The figure indicates the violent fractures of the matrix and fibers in the composites in the longitudinal direction. This may be due to the high tooth load of the tool on the workpiece at high feed rates.

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High speed machining of composite materials

Jalumedi Babu , ... João Paulo Davim , in High Speed Machining, 2020

4.5 Tool wear

In milling of CFRP composites too tool wear is observed as edge chipping and abrasion [1]. Tool wear depends on length of cut and cutting conditions. This tool wear shows direct relations with the cutting forces and temperatures. Greater length of cut leads to tool wear and results in higher thrust force and temperatures as shown in Figs. 3.30 and 3.31. It can be noted that at higher spindle speeds thrust forces are low because of matrix softening due to higher temperatures.

Figure 3.30. Influence of the tool wear at different spindle speed for a feed rate of 1000 mm/min (A) feed force and (B) transverse force [1].

Figure 3.31. Influence the tool wear on temperature at different spindle speeds for feed rates of (A) 250 and (B) 1000 mm/min [1].

Uhlmanna et al. [33] could machine CFRP laminate at a spindle speed of 60,000 rpm with machining velocities up to 1500 m/min and feed rate 12 m/min. Their results confirm that with high speed machining productivity can be increased up to 300% when compared with conventional machining as shown in Fig. 3.32.

Figure 3.32. Productivity of high speed milling and comparison with conventional milling and other machining processes [33].

Recent works of Seok et al. [34] open a new dimension to high speed machining with speeds up to 80,000 rpm with low-temperature machining with a vortex tube that injects the air at −20 °C. They use dry ice as a refrigerant. This work concludes that the HSC with low-temperature environment reduces the machining temperatures and cutting forces and results in defects-free machining of composites.

Earlier sections conclude that high speed milling not only increases the productivity but also reduces the machining defects. High speed machining with low temperature has good scope for machining of composite materials. This will enhance the productivity further and, at the same time, minimize the defects.

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Material profiles

Michael F. Ashby , in Materials and the Environment (Second Edition), 2013

CFRP (Isotropic)

The material. Carbon fiber reinforced polymer (CFRP) composites offer greater stiffness and strength than any other type, but they are considerably more expensive than glass fiber reinforced polymer (GFRP). Continuous fibers in a polyester or epoxy matrix give the highest performance. The fibers carry the mechanical loads, while the matrix material transmits loads to the fibers and provides ductility and toughness as well as protecting the fibers from damage caused by handling or the environment. It is the matrix material that limits the service temperature and processing conditions.

Composition

Epoxy+continuous HS carbon fiber reinforcement (0, + −45, 90), quasi-isotropic lay-up

General properties
Density	1,500	–	1,600	kg/m3
Price	40.0	–	44.0	USD/kg

Mechanical properties
Young's modulus	69	–	150	GPa
Yield strength (elastic limit)	550	–	1,050	MPa
Tensile strength	550	–	1,050	MPa
Elongation	0.32	–	0.35	%
Hardness—Vickers	10.8	–	21.5	HV
Fatigue strength at 107 cycles	150	–	300	MPa
Fracture toughness	6.12	–	20	MPa·m1/2

Thermal properties
Maximum service temperature	140	–	220	°C
Thermal conductor or insulator?	Poor insulator
Thermal conductivity	1.28	–	2.6	W/m·K
Specific heat capacity	902	–	1,037	J/kg·K
Thermal expansion coefficient	1	–	4	µstrain/°C

Electrical properties
Electrical conductor or insulator?	Poor conductor
Electrical resistivity	1.65×105	–	9.46×105	µohm·cm

A CFRP bike frame, courtesy TREK

Eco properties: material
Global production, main component	2.8×104			metric ton/yr
Embodied energy, primary production	450	–	500	MJ/kg
CO2 footprint, primary production	33	–	36	kg/kg
Water usage	360	–	1,367	L/kg

Eco properties: processing
Simple composite molding energy	9	–	12.9	MJ/kg
Simple composite molding CO2	0.77	–	0.89	kg/kg
Advanced composite molding energy	21	–	23	MJ/kg
Advanced composite molding CO2	1.7	–	1.8	kg/kg

End of life
Recycle fraction in current supply	0	–		%
Heat of combustion	31	–	33	MJ/kg
Combustion CO2	3.1	–	3.3	kg/kg

Typical uses. Lightweight structural members in aerospace, ground transportation, and sports equipment such as bikes, golf clubs, oars, boats, and racquets; springs; pressure vessels.

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HIGH-FREQUENCY VIBRATION SHM WITH PWAS MODAL SENSORS – THE ELECTROMECHANICAL IMPEDANCE METHOD

Victor Giurgiutiu , in Structural Health Monitoring, 2008

PWAS installation and monitoring

Eighteen PWAS transducers were applied to the CFRP composite overlay after the composite overlay was attached to the RC beam soffit. The PWAS were 25-mm diameter. 0.2-mm thick, and weighed only 4 grams. The PWAS were placed along the soffit a pitch of I52-mm, symmetrical about the beam centerline (Fig. 9.41a). The PWAS installation followed the procedure provided by Measurements Group. Inc. for the installation of electrical resistance strain gages. Three-meter lead wires were attached to each PWAS to allow measurement from a safe distance away from the specimen.

FIGURE 9.41. Installation of PWAS disbond sensors for the large-scale tests of the RC beam reinforced with a CFRP composite overlay strip: (a) location and numbering (not to scale; PWAS #35 damaged during installation, replaced with PWAS #36); (b) photo of the experimental setup showing the installation and location of the PWAS disbond sensors.

The E/M impedance of each PWAS was recorded with an HP4I94A impedance analyzer. A custom Lab VIEW program interfaced with the HP4194A was used for data collection. Baseline readings were taken with all the instrumentation in place just before the start of the loading cycles, and after the first two loading cycles (N = 1 and 2). Because the first loading cycle resulted in initial (expected) cracking of the beam and some settling of the specimen on the test frame, the measurements from the second cycle (N = 2) were retained as the baseline for future comparison.

During the fatigue test, E/M impedance readings were taken at 300, 500, 600,700, 800 kilocycles and after the 807 kilocycles final failure. After each reading was completed, the data from each PWAS was processed and analyzed to determine if any change or shift had occurred between the previous lest and the present one. If a change was delected, the specimen was inspected visually for cracking or delamination, which might correspond to the change detected by the PWAS. The purpose of the visual inspection was to develop a method of predicting, through analysis of the PWAS data, the location, direction, and rate of disbonding between the CFRP overlay and the beam substrate.

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Rehabilitation and service life estimation of bridge superstructures

L.S. Lee , in Service Life Estimation and Extension of Civil Engineering Structures, 2011

4.2.4 Adhesively bonded prefabricated carbon fiber reinforced polymer (CFRP) composite

For adhesive bonding, prefabricated (pultruded) CFRP composite strips are typically precut to precise dimensions for each location. A two-component epoxy adhesive is mixed using a mechanical mixer incorporating shearing action and, once mixed, the adhesive is applied to the surface of the deck slab and the prefabricated strip, as shown in Fig. 4.3. The prefabricated CFRP strips are bonded by applying pressure in a continuous manner from one end of the pultruded strip to the opposite end, in the fiber direction, as shown in Fig. 4.4. Typically, uniform pressure is applied on the CFRP strip using a polyurethane roller, and excess adhesive is removed using a squeegee edge.

4.3. Mixing and application of epoxy adhesive.

4.4. Bonding of pultruded CFRP strips to deck soffit.

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Moisture measurement and effects on properties of marine composites

H.N. Dhakal , ... Z.Y. Zhang , in Marine Applications of Advanced Fibre-Reinforced Composites, 2016

5.2.1 Conventional fibres as reinforcements

Typical conventional reinforcements for composites include glass and carbon fibre. Glass/carbon fibre reinforced polymer composites have several advantages over their metal matrix counterparts, most notably recognised for being lightweight, corrosion resistant, high strength with increased 'strength-to-weight ratio'. E-glass fibres are one of the most important reinforcing fibres for polymer composites. However, glass fibres have some disadvantages. They are non-renewable and give problems with respect to ultimate disposal at the end of their service life since energy reclamation through incineration cannot be achieved. In addition, humid and wet environments have negligible influence on carbon and glass fibre. However, hydrophilic aramid fibres are similar to natural fibres being susceptible to moisture related degradation. This is due to an abundance of hydroxyl bond sites in natural fibres and amide groups in aramid fibres respectively which also make them susceptible to UV degradation. From this, it can be shown that both synthetic and natural reinforcements need careful consideration during material selection and application (Maxwell et al., 2005; Prasanth et al., 2013; Singh and Sharma, 2008).

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Interface Science and Composites

Soo-Jin Park , Min-Kang Seo , in Interface Science and Technology, 2011

8.8.2.1.1 Porosity

Porosity is a perennial problem in composite manufacturing, especially for laminated structures, such as carbon fiber–reinforced polymer composites. The term porosity generally refers to the voids caused by the trapped air or the volatile gas that is released during the cure process. The size and shape and distribution of the voids depend on the structure of the composites.

The presence of porosity has been shown to have a strong correlation with certain mechanical properties [201–203]. It has generally been found that the interlaminar shear strength decreases by approximately 7% per 1% of voids up to a total void content of about 4% [204]. Other mechanical properties are also affected. The 2% porosity has commonly become the nominal acceptance threshold for many composite components. Research programs in nondestructive evaluation have therefore concentrated on providing techniques that could detect and measure porosity in the range of 1%–5% (v/v). A nondestructive evaluation technique that could determine the level of porosity in a composite laminate independent of other variables, such as pore morphology and the fiber and matrix materials, would be ideal. However, to date no single nondestructive evaluation method has been able to provide this universal porosity meter.

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Lifetime Predictions of Plastics

James A. Harvey , in Handbook of Environmental Degradation of Materials (Second Edition), 2012

3.2 Master Curves

One of the most useful analytical techniques for determining lifetime predictions is the generation of master curves utilizing the dynamic mechanical analyzer (DMA). This technique involves time-temperature superimposition (TTS).

In polymer literature, a set of experimental curves can frequently be translated along a given direction to form a master curve. One of the most famous examples is the time-temperature superimposition, where the translation is generally performed along the horizontal axis. The superimposition of the different experimental curves is normally made graphically, leading to some ambiguities in the construction of the master curve and in the determination of the translation paths. Starting from the analytical conditions to be satisfied by a set of curves that were related by a translation along a given direction, a computer program can be developed to obtain the master curve from a set of experimental data. Finally, some examples can be obtained of the applicability of the computer program developed for simulated storage, shear compliance, viscosity against shear rate, and stress relaxation data. ²

Dynamic mechanical testing involves subjecting the plastic specimen to an alternating strain, and simultaneously measuring the stress. For linear viscoelastic behavior, at equilibrium, stress and strain vary sinusoidally, but the strain lags behind the stress. Thus we write

(3.1) $\mathrm{strain}e=e_{\mathrm{o}}\sin \mathrm{\omega }t$

and

(3.2) $\mathrm{strain}\mathrm{\sigma }={\mathrm{\sigma }}_{\mathrm{o}}\sin (\mathrm{\omega }t+\mathrm{\delta })\text{,}$

where ω is the angular frequency and the δ the phase lag.

Thus, we can we can rewrite stress to be equal to

(3.3) $\mathrm{\sigma }={\mathrm{\sigma }}_{\mathrm{o}}\sin \mathrm{\omega }t\cos \mathrm{\delta }+{\mathrm{\sigma }}_{\mathrm{o}}\cos \mathrm{\omega }t\sin \mathrm{\delta }.$

Stress has two components: (1) magnitude (σ_ocosδ) in phase with the strain; and (2) magnitude (σ_osinδ) out of phase with the strain.

Now we may define two new quantities: G ₁ is in phase with the strain, and the quantity G ₂ is 90 degrees out of phase with the strain. We may rewrite strain as

(3.4) $\mathrm{\sigma }=e_{\mathrm{o}}{G}_1\sin \mathrm{\omega }t+e_{\mathrm{o}}{G}_2\cos \mathrm{\omega }t\text{,}$

where

$G_1=({\mathrm{\sigma }}_{\mathrm{o}}/e_{\mathrm{o}})\cos \mathrm{\delta }\mathrm{and}{G}_2=({\mathrm{\sigma }}_{\mathrm{o}}/e_{\mathrm{o}})\sin \mathrm{\delta }.$

If we construct a phasor diagram (see Figure 3.1) with G ₁ and G ₂, we may define a new quantity G*, complex modulus.

Figure 3.1. Phasor diagram for complex modulus G*=G ₁+iG ₂ and phase lag, tan δ||I||=G₂/G ₁.

If e=e _o, exp(iω t), then σ=σ_o exp[i(ωt+δ)], so that

(3.5) $G^{*}=\mathrm{\sigma }/e=({\mathrm{\sigma }}_{\mathrm{o}}/e_{\mathrm{o}})\exp (\mathrm{i}\mathrm{\delta })$

(3.6) $={\mathrm{\sigma }}_{\mathrm{o}}/e_{\mathrm{o}}(\cos \mathrm{\delta }+\mathrm{isin}\mathrm{\delta })$

(3.7) $=G_1+G_2\text{,}$

where G ₁ which is in phase with the strain, is called the storage modulus because it defines the energy stored in the specimen due to the applied strain, and G ₂, which is π/2 out of phase with the strain, defines the dissipation of energy and is referred to as the loss modulus. The energy (ΔE) dissipated per cycle can be defined as

(3.8) $\mathrm{\Delta }E=\int (\mathrm{\sigma }\mathrm{d}e)={\int }_0^{2\mathrm{\pi }\mathrm{\omega }}(\mathrm{\sigma }(\mathrm{d}e/\mathrm{d}t)\mathrm{d}t.$

Substituting for stress and strain, solving the integration, and evaluating ΔE over a quarter cycle rather than the entire period, we can reduce the variables to

(3.9) $E=1/2(G_1{e}_{\mathrm{o}}^2)$

which is independent of frequency.

G ₁ and G ₂ can rewritten as

$G_1=(2E/e_{\mathrm{o}}^2).$

and

$G_2=(\mathrm{\Delta }E/\mathrm{\pi }{e}_{\mathrm{o}}^2).$

Hence,

(3.10) $G_2/G_1=\tan \mathrm{\delta }=\mathrm{\delta }E/(2\mathrm{\pi }E).$

The ratio ΔE/E is called the specific loss

(3.11) $\mathrm{\Delta }E/E=2\mathrm{\pi }\tan \mathrm{\delta }.$

Typical values of G ₁ G ₂ and tanδ for a polymer are 10⁹  Pa, 10⁷  Pa, and 0.01, respectively. In such cases, |G*| is approximately equal to G ₁ . It is customary to define the dynamic mechanical behavior in terms of the "modulus," G ₁ and the phase angle, δ, or tanδ=G ₂/G ₁.

A complementary treatment can be developed to define a complex compliance, J*=J ₁–iJ ₂, which is directly related to the complex modulus, as G*=1/J*. Consider the variation of G ₁ G ₂ and tanδ with frequency for a viscoelastic solid that shows no flow (Figure 3.2). At very low frequencies, the polymer is rubber-like and has a low modulus (G ₁ is probably about 10⁵  Pa), which is independent of frequency. At the highest frequencies, the rubber is glassy, with a modulus around 10⁹  Pa, which is again independent of frequency. In the intermediate region, where the material behaves viscoelastically, the modulus will increase with increasing frequency. The loss modulus will be zero at low and high frequencies, where stress and strain are in phase for the rubbery and glassy states. In the intermediate viscoelastic region, G ₂ rises to a maximum value, close to the frequency at which G ₁ is changing most rapidly with frequency. The loss factor, tanδ, also has a maximum in the viscoelastic region, but this occurs at a slightly lower frequency than that in G ₂, since tanδ=G₂/G ₁, and G ₁ is also changing rapidly in that frequency region. An analogous diagram shows the variation of the compliances J ₁ and J ₂ with frequency. ³

Figure 3.2. The complex modulus G*=G ₁+iG ₂ as a function of frequency. ³

Professors Miyano and Kimpara and their groups at Kanazawa Institute of Technology have proposed an accelerating testing methodology for assessing long-term mechanical performance of carbon fiber reinforced polymer (CFRP) composites. The methodology was composed of constructing the master curve for several deformation modes based on four hypotheses:

1.

Same failure mechanisms of CFRP composites under constant strain rate (CSR), creep and cyclic loading over the same time and temperature, which is controlled by the viscoelastic instability of polymer resins

2.

Same time-temperature superimposition principle for all the failure modes

3.

Linear cumulative damage law for monotonic loading

4.

Linear dependence of fatigue strength under various stress ratios (R _s =σ_min/σ_max)

The master curves for CSR, creep (constant loading), and fatigue tests were constructed by applying the time-temperature superimposition principle. The variations of the CSR strength (σ_s), creep strength (σ_c) and fatigue strength (σ_f) to the time to failure (t _s , t_c and t _f ) is shifted by the time-temperature shift factor [a _To (T)] given in Eq. (3.12), which is independent of the loading modes.

(3.12) $a_{\mathit{T}\mathrm{o}}(\mathit{T})\exp [\mathrm{\Delta }H/2.3R(1/T(1/T_{\mathrm{o}})]\text{,}$

where R is the gas constant and T _o is the reference temperature. The value of ΔH for the CFRP failure and storage modulus of the polymer resin are found to be identical due to the failure mechanism of CFRP composites controlled by the viscoelastic flow of polymer resins. To determine the master curves [σs ( ${t\prime }_{\mathrm{s}}:$ T _o), σ_c( ${t\prime }_c:$ T _o) and σ_f( ${t\prime }_f:$ R _s, f, T _o)], the reduced failure time ( ${t\prime }_s\text{,}{t\prime }_c:$ and ${t\prime }_f$ ) is defined by

(3.13a) ${t\prime }_s=t_s/a_{T\mathrm{o}}(T)\mathrm{for}\text{CSR}\text{,}$

(3.13b) ${t\prime }_c={\mathit{t}}_{\mathit{c}}/a_{T\mathrm{o}}(T)\mathrm{for}\text{creep}\text{,}$

and

(3.13c) ${t\prime }_f=t_{\mathrm{f}}/a_{T\mathrm{o}}(T)=N_f/f{a}_{T\mathrm{o}}(T)=N_f/f\prime \mathrm{for}\mathrm{fatigue}\text{,}$

where N _f is the number of cycles to failure and f is the frequency of cyclic loading. The master curve can be applied in a wide temperature range above and below the glass transition temperature, although ΔH becomes different, depending on the polymer structure. For the CSR tests, the variations of σ_s to t _s are measured under various loading rates and temperatures. For the creep test, t _c is determined as a function of constant σ_c at various temperatures. Different cumulative damage proceeds in CFRP composites subjected to rising (CSR) and constant (creep) loading. In order to estimate t _c from the CSR tests, linear cumulative damage for monotonic loading (approximated stepwise) is defined by

${\int }_0^{t*}\mathrm{d}\mathrm{t}/{\mathrm{t}}_{\mathrm{c}}[\mathrm{\sigma }(\mathrm{t})]=\mathrm{\Sigma }\underset{\mathrm{i}}{\overset{2\mathrm{n}-1}{\mathrm{\Delta }\mathrm{t}/{\mathrm{t}}_{\mathrm{c}}}}[{\mathrm{\sigma }}_{\mathrm{i}}(\mathrm{t})]=[{\mathrm{t}}_{\mathrm{s}}({\mathrm{\sigma }}_{2\mathrm{n}})/\mathrm{n}]$

(3.14) $[1/{\mathrm{t}}_{\mathrm{c}}({\mathrm{\sigma }}_1)+\dots .+1/{\mathrm{t}}_{\mathrm{c}}({\mathrm{\sigma }}_{2\mathrm{n}-1})]-1\text{,}$

where t* [=t _s (σ_2n)] is the failure time under stress history, Δt (=t*/n) is the time interval for stepwise loading, and t _c [σ_i(t)] is the creep failure time under σ_i(t). Thus, t _c (σ_2n−1) can be determined from t _s (σ_2n−2) and t _s (σ_2n) using Eq. (3.15) derived from Eq. (3.14):

(3.15) ${\mathrm{t}}_{\mathrm{c}}({\mathrm{\sigma }}_{2\mathrm{n}–1})={\mathrm{t}}_{\mathrm{s}}({\mathrm{\sigma }}_{2\mathrm{n}}){\mathrm{t}}_{\mathrm{s}}({\mathrm{\sigma }}_{\mathrm{2n}–2})/[\mathrm{n}{\mathrm{t}}_{\mathrm{s}}({\mathrm{\sigma }}_{\mathrm{2n}–2})–(\mathrm{n}–1){\mathrm{t}}_{\mathrm{s}}({\mathrm{\sigma }}_{2\mathrm{n}})]$

The linear cumulative damage law for the loading history [hypothesis (c)] has been proven by good agreement of the master curves for the CRS and creep observed in many CFRC systems.

In order to construct the fatigue master curve, the value of t _f is converted from N _f using f, and ${t\prime }_f$ is defined by the shifted frequency (f′) Eq. (3.13c). Moreover, changing f and R _s , as well as temperatures, affects the relationships of σ_f to ${t\prime }_f$ . By applying a linear dependence of the fatigue strength on R _s [hypothesis (d)], the fatigue master curve [σ_f (t _f : R _s , f, T)] for the various R_s is estimated by

(3.16) ${\mathrm{\sigma }}_f(t_f:R_s\text{,}f\text{,}T)={\mathrm{\sigma }}_{f:1}(t_f:f\text{,}T)R_s+{\mathrm{\sigma }}_{f:0}(t_f:f\text{,}T)(1–R_s)\text{,}$

where σ_f:1 is the fatigue strength for R _s =1 and σ_f:0 is the CSR strength (R _s =0, N _f=1/2 or t _f =1/2f). As N _f is increased, σ_f drastically decreases when ${t\prime }_f$ is relatively short.

The hypothesis (d) is verified by series of fatigue experiments performed under various R _s . The applicability of the hypotheses (a–d) for several CFRP composite systems is summarized in Table 3.1. In various GFRP/metal joining systems (conical shaped joints, brittle and ductile adhesive joints, and bolted joints), it is possible to construct the master curves as well. Based on the study performed, it is unequivocal that the accelerating testing methodology is applicable when polymer resins fracture in a brittle manner and the deformation behavior in carbon fibers is time independent. Moreover, the environmental degradation of CFRP composites can be assessed using the time-temperature-water adsorption superimposition principle.

Table 3.1. Applicability of Master Curve for Various CFRP Composites Subjected to Various Loading Modes ⁴

Fiber		Matrix	Type	Fiber/matrix	Loading Mode	Hypothesis
						a	b	c	d
Carbon	PAN	Epoxy	UD	T400/828	LT	O	O	O	O
				T300/2500	LB	O	O	O	O
					TB	O	O	O	O
			SW	T400/3601	LB	O	O	O	O
		PEEK	UD	T300/PEEK	LB	O	x	x	Δ
					TB	Δ	x	x	x
	Pitch	Epoxy	UD	XN40/25C	LB	O	Δ	x	O
Glass		Epoxy	SW	E-glass/epoxy	LB	O	Δ	O	x
		Vinylester	PW	E-glass/vinylester	LB	O	O	O	x

Type of fibers: UD: Unidirectional, SW: Strain woven, PW: Plain woven.

Loading modes: LT: Longitudinal tension, LB: Longitudinal bending, TB: transverse bending.

Polymer-modified asphalt is a highly temperature sensitive material. To obtain the master curves, the material was tested over a temperature interval from −30   °C to at least 90   °C. Since the polymer-modified asphalt undergoes the transition from a glass-like to a Newtonian-like material in this temperature range, three testing geometries were studied. The geometries used were as follows: plate-plate (PP) for the mid-range temperatures; torsion bar (TB) for the low temperatures; and bob and cup (BC) for the high temperatures. The shift from one fixture to another must be done at a temperature that depends on the viscoelastic properties of the material. In the case of asphalt, it is theoretically possible to measure rheological properties using PP for the whole range of temperatures. However, when close to the glass transition temperature, slippage and breakage can occur, thus leading to very scattered and noisy data. Such problems were eliminated with TB. On the other hand, close to room temperature asphalt started to become soft so it was unable to support its own weight and keep the bar shape; whereas slipping and breaking were no longer a problem for PP. Plate-plate and BC geometries remained the best until the material approached the liquid state. In this case, the problems were the tendency to flow out from the space between the plates and the low torque values (due to the limited PP surface). Both problems were solved with a BC fixture. In conclusion, this paper showed examples of how isotherms obtained with three sample geometries and two rheometers followed the time-temperature-superimposition principle. This gave a solid confirmation of how data from different sources was combined to build reliable master curves covering a very wide range of reduced frequency. Master curves obtained from these geometries covered up to 20 decades of reduced frequencies. ⁵

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Machining processes utilizing mechanical energy

Bijoy Bhattacharyya , Biswanath Doloi , in Modern Machining Technology, 2020

3.1.8.2 Rotary ultrasonic machining

Applications of rotary ultrasonic machining process are given as follows:

(i)

Rotary ultrasonic machining (RUM) has a wide range of applications in present day industries such as aircrafts, automobiles, sports goods, medical tools, computers, electronics, optical, etc. [11].

(ii)

RUM can machine ceramic materials like zirconia and glass ceramics used for automotive and optical industries.

(iii)

It can machine carbon fiber reinforced polymer (CFRP) composites that has wide applications in aircrafts, automotive industries and also in the fabrication of engine blades.

(iv)

It can machine titanium and its alloys, which have been used in the fabrication of turbine parts such as rotors, stator and compressor blades, etc.

(v)

It can machine stainless steel used for various applications such as in automobile, medical tools manufacturing and house appliances.

(vi)

It is capable of machining of engineering metals and alloys, dental ceramics such as macor and dental zirconia as used in dental restorations.

(vii)

It can machine sapphire (alumina in single crystal form), generally applicable in the electronics fields, particularly in the fabrication of chips and circuits, etc.

(viii)

It can process optical and brittle materials such as K9 and BK7 glass for complex shape generation in various applications.

(ix)

RUM process can be applied for various machining operations such as drilling, milling, turning, grinding, surface texturing and finishing operations.

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Sustainable fibre-reinforced polymer composites in construction

M. Fan , in Management, Recycling and Reuse of Waste Composites, 2010

Advanced composite strengthened RC beams

FRP composites can be used to strengthen RC beams. Their use for this purpose is gradually usurping the former, traditional techniques of flitching with steel plates or corseting with steel jackets (steel is susceptible to corrosion which often causes serious deterioration of bonds at the steel–concrete interface; what is more, addition of steel increases both the self-weight and the overall cross-sectional dimensions of the structures to which it is attached). FRP composite plates are usually bonded to the tension side of RC beams with epoxy resin in order to increase the flexural strength of the beams. The fibres in the composite are placed parallel to the principal stress direction, which is normally perpendicular to the cracks. Shear strengthening of RC beams is achieved by bonding composite reinforcement with fibres parallel to the direction of the shear stresses (Fig. 19.7). The efficacy of the strengthening depends on the property and geometry of reinforcement (i.e. FRP composites), configuration of lamination and loading (i.e. the number of and wrapping schemes of layers, and the percentage of reinforcement, shear span to depth). The flexural strength of the strengthened RC could be increased by as much as 40% with glass fibre reinforced polymer (GFRP) composite and 200% with carbon fibre reinforced polymer (CFRP) composite reinforcement. Shear strength of RC beams may be increased by 60–120% depending on the materials specified and the architecture of the reinforcing fibres (Heffernan and Erki, 1996; Bonacci and Maalej, 2000, 2001; Karbhari and Zhao, 1998; Shahawy et al., 2001; Shin and Lee, 2003; Brena and Macri, 2004). The fatigue life of RC beams could also be significantly extended by carefully configured use of externally bonded CFRP composite laminate (Barnes and Mays, 1999; Erki and Meier, 1999; Shahawy and Beitelman, 1999; Masoud et al., 2001; Heffernan and Erki, 2004).

19.7. Strengthening of concrete beam.

However, the strengthened RC can exhibit greater deflection under load owing to the lower modulus of elasticity of FRP composites as compared with steel reinforcement. A number of techniques for improvement of ductility have been studied, including an anchorage system and the inclusion of innovative tri-axially braided ductile fabric (White et al., 2001; Grace et al., 2002; Salom et al., 2004).

Complex interactions between concrete and steel and reinforcements create major obstacles to the development of analytical formulae to predict the behaviour of strengthened beams and columns. A number of analytical models have been proposed, such as the simplified linear elastic models (strain compatibility) and non-linear finite element models for the flexural behaviour and interfacial failure analysis of strengthened RC beams (Ziraba et al., 1994; Vijay and GangaRao, 2001; Teng et al., 2003). The ultimate shear capacity of strengthened beams has been calculated by assuming linear elastic behaviour of reinforcement materials (Gendron et al., 1999; Ibell and Burgoyne, 1999; Triantafillou and Antonopoulos, 2000) or by compression field theory through assuming a perfect bond between concrete and reinforcement (Malek and Saadatmanesh, 1998a,b).

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