4 Residual stresses in composite materials Manufacturing processes,such as shot peening,chemical surface treatment and laser surface hardening,are used to induce useful surface compression to improve resistance to fatigue failure.However,those leading to surface tension normally facilitate the formation of cracks,which can cause untimely fracture (Colpo, 2006;Fitzpatrick and Lodini,2003).The distortion of laminate composites is typically the result of residual stresses.This makes it particularly important to understand,measure,model and control residual stresses in composite and other materials. Residual stresses arise for several reasons:on the macroscopic scale,they may emanate from heat treating,machining and secondary processing,and assembly. On the microscopic scale,they usually result from the discontinuities between the thermal expansion coefficients,yield stresses,rigidities or phase changes (e.g cure shrinking)of different constituents.In any component or material,both kind of stress may co-exist (Colpo,2006). A fiber reinforced polymer(FRP)composite is usually subject to a process wherein the resin is heated,the fibers are wetted and cure is performed at high temperatures.The need for high temperatures in the curing process results in formation of residual stresses in the final laminate structure.These residual stresses have two major causes:the mismatch in thermal expansion of the constituents,and chemical shrinkage of the polymers in the composite. Measurement and characterization of these stresses is complex (Liu,1999). Residual stresses typically arise due to the discrepancies between the mechanical properties of the matrix and the reinforcing fibers.Other mechanisms that cause residual stresses include cure shrinkage,moisture,ageing,elevated post-cure temperature,differences in material properties at the microscopic scale,differences in fiber volume across the matrix and non-uniform degree of cure (Tsouvalis etal.,2009). 1.2 Categories of residual stresses Barnes and Byerly(1994)explained the various types of residual stress at work in continuous carbon-fiber-reinforced thermoplastic composites.They identified three levels of stress in laminated structures:the 'micro-stresses'present between distinct fibers within each ply,the 'macro-stresses'forming in multi-axial laminates at the ply-to-ply scale,and a third,more prevalent level of stress resulting from different thermal histories of distinct parts of a laminate during the cooling stage. The discontinuity between the thermal expansion coefficients of the fiber and matrix,along with the development of chemical shrinkage,create residual strains and stress at the ply scale.As a lamina is cured,its matrix constituent is subject to polymerization.Epoxy resins undergo condensation polymerization,where two reacting monomers are put together to form a new molecule of the compound in question (Gibson,1994).For many advanced structural composites,this process Woodhead Publishing Limited,2014
4 Residual stresses in composite materials © Woodhead Publishing Limited, 2014 Manufacturing processes, such as shot peening, chemical surface treatment and laser surface hardening, are used to induce useful surface compression to improve resistance to fatigue failure. However, those leading to surface tension normally facilitate the formation of cracks, which can cause untimely fracture (Colpo, 2006; Fitzpatrick and Lodini, 2003). The distortion of laminate composites is typically the result of residual stresses. This makes it particularly important to understand, measure, model and control residual stresses in composite and other materials. Residual stresses arise for several reasons: on the macroscopic scale, they may emanate from heat treating, machining and secondary processing, and assembly. On the microscopic scale, they usually result from the discontinuities between the thermal expansion coeffi cients, yield stresses, rigidities or phase changes (e.g. cure shrinking) of different constituents. In any component or material, both kind of stress may co- exist (Colpo, 2006). A fi ber reinforced polymer (FRP) composite is usually subject to a process wherein the resin is heated, the fi bers are wetted and cure is performed at high temperatures. The need for high temperatures in the curing process results in formation of residual stresses in the fi nal laminate structure. These residual stresses have two major causes: the mismatch in thermal expansion of the constituents, and chemical shrinkage of the polymers in the composite. Measurement and characterization of these stresses is complex (Liu, 1999). Residual stresses typically arise due to the discrepancies between the mechanical properties of the matrix and the reinforcing fi bers. Other mechanisms that cause residual stresses include cure shrinkage, moisture, ageing, elevated post- cure temperature, differences in material properties at the microscopic scale, differences in fi ber volume across the matrix and non- uniform degree of cure (Tsouvalis et al. , 2009). 1.2 Categories of residual stresses Barnes and Byerly (1994) explained the various types of residual stress at work in continuous carbon- fi ber-reinforced thermoplastic composites. They identifi ed three levels of stress in laminated structures: the ‘micro- stresses’ present between distinct fi bers within each ply, the ‘macro- stresses’ forming in multi- axial laminates at the ply- to-ply scale, and a third, more prevalent level of stress resulting from different thermal histories of distinct parts of a laminate during the cooling stage. The discontinuity between the thermal expansion coeffi cients of the fi ber and matrix, along with the development of chemical shrinkage, create residual strains and stress at the ply scale. As a lamina is cured, its matrix constituent is subject to polymerization. Epoxy resins undergo condensation polymerization, where two reacting monomers are put together to form a new molecule of the compound in question (Gibson, 1994). For many advanced structural composites, this process
The importance of measuring residual stresses 5 happens in two steps.Prepreg tape is produced by wetting the fibers and allowing the matrix to partially cure.When these prepreg materials are arranged into the desired stacking sequences and then heated to the desired cure temperature, the polymerization process is complete.During this process,the matrix undergoes a volumetric change known as chemical shrinkage,while the fibers stay volumetrically unchanged.This heightens the mismatch in expansion of the fibers and matrix,where the matrix undergoes greater expansion and contraction than the fiber (Myers,2004). Residual stresses arise when the expansion of the lamina is limited.As the angles of the lamina vary from ply to ply,the lower contraction of the fiber constrains the contraction of the matrix.When temperatures are lowered,the matrix attempts to contract but is subjected to tensile stress opposing this deformation.If all of the fibers are aligned with each other,there will be no stress on the ply scale.A cross-ply [0/90]stacking sequence leads to the highest level of residual stress(Myers,2004). All three scales ofresidual stresses must be taken into account when determining the overall state of stress.At the macro-or structural-scale,residual stresses arise due to the counteraction of one part of the structure against another,which may occur when one component experiences different thermal strains from another,or because of external constraints.At the meso-or laminate-scale. residual stresses arise through individual laminae experiencing different thermal and hygroscopic strains from those of neighboring laminae.This may be due to temperature and moisture variation throughout the laminate and from inter- lamina differences in material characteristics or orientations.The fibers and matrix are equally strained at both the macro-and meso-scales;therefore,the effects of residual stresses at these scales are not distinguishable from mechanical stresses.However,at the micro-or lamina-scale,this does not hold true.At this scale,stresses in the fiber and matrix counteract,even when the lamina appears not to be loaded at larger scales.In this situation the residual stresses arise from discrepancies in the unconstrained thermal and hygroscopic strains of the fibers and the matrix. Polymerization cure shrinkage of the matrix sets up additional residual stresses at this scale.Residual stresses are set up both parallel and perpendicular to the fiber direction.Nevertheless,the fibers can significantly restrain the free movement of the resin system and align it with the fiber length.The stresses in this direction are thereby considerably greater than those perpendicular to the fiber direction.Consequently,the magnitude of the latter stresses is not important,particularly as these stresses are not aligned in a direction to increase environmentally assisted cracking of the laminate (Reid and Paskaramoorthy,2009). The residual stresses at the micro-scale,along with the overall stress state arising from both the mechanical loading and the macro-and meso-scale residual stresses,alter the overall stress state.Tensile residual stresses at the micro-scale Woodhead Publishing Limited,2014
The importance of measuring residual stresses 5 © Woodhead Publishing Limited, 2014 happens in two steps. Prepreg tape is produced by wetting the fi bers and allowing the matrix to partially cure. When these prepreg materials are arranged into the desired stacking sequences and then heated to the desired cure temperature, the polymerization process is complete. During this process, the matrix undergoes a volumetric change known as chemical shrinkage, while the fi bers stay volumetrically unchanged. This heightens the mismatch in expansion of the fi bers and matrix, where the matrix undergoes greater expansion and contraction than the fi ber (Myers, 2004). Residual stresses arise when the expansion of the lamina is limited. As the angles of the lamina vary from ply to ply, the lower contraction of the fi ber constrains the contraction of the matrix. When temperatures are lowered, the matrix attempts to contract but is subjected to tensile stress opposing this deformation. If all of the fi bers are aligned with each other, there will be no stress on the ply scale. A cross- ply [0/90] stacking sequence leads to the highest level of residual stress (Myers, 2004). All three scales of residual stresses must be taken into account when determining the overall state of stress. At the macro- or structural- scale, residual stresses arise due to the counteraction of one part of the structure against another, which may occur when one component experiences different thermal strains from another, or because of external constraints. At the meso- or laminate- scale, residual stresses arise through individual laminae experiencing different thermal and hygroscopic strains from those of neighboring laminae. This may be due to temperature and moisture variation throughout the laminate and from interlamina differences in material characteristics or orientations. The fi bers and matrix are equally strained at both the macro- and meso- scales; therefore, the effects of residual stresses at these scales are not distinguishable from mechanical stresses. However, at the micro- or lamina- scale, this does not hold true. At this scale, stresses in the fi ber and matrix counteract, even when the lamina appears not to be loaded at larger scales. In this situation the residual stresses arise from discrepancies in the unconstrained thermal and hygroscopic strains of the fi bers and the matrix. Polymerization cure shrinkage of the matrix sets up additional residual stresses at this scale. Residual stresses are set up both parallel and perpendicular to the fi ber direction. Nevertheless, the fi bers can signifi cantly restrain the free movement of the resin system and align it with the fi ber length. The stresses in this direction are thereby considerably greater than those perpendicular to the fi ber direction. Consequently, the magnitude of the latter stresses is not important, particularly as these stresses are not aligned in a direction to increase environmentally assisted cracking of the laminate (Reid and Paskaramoorthy, 2009). The residual stresses at the micro- scale, along with the overall stress state arising from both the mechanical loading and the macro- and meso- scale residual stresses, alter the overall stress state. Tensile residual stresses at the micro- scale
6 Residual stresses in composite materials tend to assist in opening microcracks in the polymer matrix before the crack may promote the flow of corrosive media to the glass fibers,potentially heightening crack growth rate.This is prevalent as corrosion equipment is usually cured at room temperature and then exposed to post-cure at higher temperatures for the enhancement of the chemical resistance of the resin system (Stone et al.,1997).Therefore,the relatively high thermal contraction of the resin system as the laminate cools to room temperature is significantly hindered by the stiff fibers.Moreover,the fibers can inhibit the free shrinkage of the resin due to the additional polymerization reactions through post-cure. Therefore the resin system is loaded in tension while the fibers become compressed. The tensile stress in the resin increases its predisposition to microcracking Furthermore,the reduction in tensile stress in the fibers lowers their tendency to fracture.As a result,the increased percolation of corrosive media to the fibers can be offset by the longer time required for flaws of critical size to form in the fibers (Reid,2009). Another basic mechanism taking place when a laminate with a low coefficient of thermal expansion(CTE)is cured on a tool with a much higher CTE,is tool-laminate interaction.Cure shrinkage is another basic mechanism creating residual stresses.It is a chemical effect occurring through curing when the polymer volume decreases leading to a high level of locked in stress (Stamatopoulos,2011). The sources of residual stresses are classifiable as intrinsic (concerning material,lay-up and structure shape)or extrinsic (concerning processing and tooling).Non-consistent thermal expansion is one of the basic mechanisms affecting all three of the above-mentioned levels of residual stresses.At the micro-mechanical (intra-laminar)level,the thermal expansion coefficient discrepancies between the fibers and the matrix is the chief factor for development of residual stresses.Cooling through the curing cycle leads to a volumetric shrinkage of the matrix considerably greater than that of the fibers.A second level of stress in continuous-fiber-reinforced composites forms on the ply-to-ply scale (inter-laminar)in multi-axial laminates,because of the non-consistent CTEs of the individual plies in different directions.These are regarded as 'macro-stresses'(macro-mechanical or lamination residual stresses according to Parlevliet et al.,2006),which exist on a ply-to-ply scale as a result of lamina anisotropy (Twigg et al.,2004).At the laminate level,residual stresses arise throughout the thickness and are typically parabolically distributed.Such stresses in uni-axial laminates can be about 40 MPa,affecting the mechanical response of the composite.Moreover,dimensional tolerance problems in asymmetrically cooled laminates might be caused by such stresses.One important point concerning the stresses arising at this level is that they can be stopped by raising the composite above the glass transition temperature (T)of the matrix,and permitting relaxation processes to take effect (Twigg et al., 2004). Woodhead Publishing Limited,2014
6 Residual stresses in composite materials © Woodhead Publishing Limited, 2014 tend to assist in opening microcracks in the polymer matrix before the crack may promote the fl ow of corrosive media to the glass fi bers, potentially heightening crack growth rate. This is prevalent as corrosion equipment is usually cured at room temperature and then exposed to post- cure at higher temperatures for the enhancement of the chemical resistance of the resin system (Stone et al. , 1997). Therefore, the relatively high thermal contraction of the resin system as the laminate cools to room temperature is signifi cantly hindered by the stiff fi bers. Moreover, the fi bers can inhibit the free shrinkage of the resin due to the additional polymerization reactions through post- cure. Therefore the resin system is loaded in tension while the fi bers become compressed. The tensile stress in the resin increases its predisposition to microcracking. Furthermore, the reduction in tensile stress in the fi bers lowers their tendency to fracture. As a result, the increased percolation of corrosive media to the fi bers can be offset by the longer time required for fl aws of critical size to form in the fi bers (Reid, 2009). Another basic mechanism taking place when a laminate with a low coeffi cient of thermal expansion (CTE) is cured on a tool with a much higher CTE, is tool- laminate interaction. Cure shrinkage is another basic mechanism creating residual stresses. It is a chemical effect occurring through curing when the polymer volume decreases leading to a high level of locked in stress (Stamatopoulos, 2011). The sources of residual stresses are classifi able as intrinsic (concerning material, lay- up and structure shape) or extrinsic (concerning processing and tooling). Non- consistent thermal expansion is one of the basic mechanisms affecting all three of the above- mentioned levels of residual stresses. At the micro- mechanical (intra- laminar) level, the thermal expansion coeffi cient discrepancies between the fi bers and the matrix is the chief factor for development of residual stresses. Cooling through the curing cycle leads to a volumetric shrinkage of the matrix considerably greater than that of the fi bers. A second level of stress in continuous- fi ber-reinforced composites forms on the ply- to-ply scale (inter- laminar) in multi- axial laminates, because of the non- consistent CTEs of the individual plies in different directions. These are regarded as ‘macro- stresses’ (macro- mechanical or lamination residual stresses according to Parlevliet et al. , 2006), which exist on a ply- to-ply scale as a result of lamina anisotropy (Twigg et al. , 2004). At the laminate level, residual stresses arise throughout the thickness and are typically parabolically distributed. Such stresses in uni- axial laminates can be about 40 MPa, affecting the mechanical response of the composite. Moreover, dimensional tolerance problems in asymmetrically cooled laminates might be caused by such stresses. One important point concerning the stresses arising at this level is that they can be stopped by raising the composite above the glass transition temperature (T g ) of the matrix, and permitting relaxation processes to take effect (Twigg et al. , 2004)
The importance of measuring residual stresses 7 1.3 Effects of residual stresses The failures of composite materials are largely associated with residual stresses. The normal residual stress of the fiber-matrix interface seriously influences fiber matrix debonding and pull-out,the most prevalent failure mechanisms(Liu et al., 1999;Nath et al.,2000;Warrier et al.,1999).Residual stress has also been proven to influence some other performance characteristics,including matrix cracking (Deve and Maloney,1991),yield strength (Nakamura and Suresh,1993;Zheng, 2000)and dimensional stability (Jain and Mai,1996). Failures through fatigue,creep,wear,stress corrosion cracking,fracture, buckling,etc.,are mainly caused by residual stresses.Furthermore,residual stresses regularly lead to dimensional instability,an example of which is distortion following heat treating or machining of a part.In parts without external loads, residual stresses can be located.All manufacturing processes can bring about residual stresses,and correlated loads are exaggerated with residual stresses. Residual stresses are subtle as they compensate equilibrium and thus remove all outer traces of their presence.It is necessary to be aware of residual stresses in all engineering structures in which safety factors are a problem,as residual stresses contribute to failures.Residual stresses brought about by different manufacturing processes can be predicted or modeled and much research is underway in this area (Prime,1999a,b). The discharges of residual stresses cause deformation,be it an inconspicuous process leading to the formation of a crack on a simple clay vase or an agitation of the Earth by a massive earthquake which causes great destruction.It is generally very difficult to predict failures resulting from residual stresses.The existence of residual stresses has a significant effect on the integrity of the mechanical components at work,in such circumstances as a nuclear reactor over an extended period of time,or in systems of high security-sensitivity,such as an airplane.The existence of residual tensile stresses close to the surface is regarded as one of the major contributing factors leading to the slow and ongoing formation of cracks in parts of objects that are exposed to radiation.Containers that are welded and sealed completely (Masubushi,1980;Prime 1999a,b)and those containing nuclear waste,the radioactive level of which continues to be dangerously high for many centuries,are more subject to these sorts of residual stresses.Machining by turning,which is an operation performed on most shafts and rods,generally causes tensile residual stresses close to the surface (Brinksmeier et al.,1982). These stresses are destructive to fatigue life under the pressure of cyclic loads.In addition,the compressive residual stress present close to the surface has been proven to lengthen fatigue life and prevent stress corrosion cracking (Cheng and Finnie,2007). Not only does residual stress affect the formation of surface cracks,it also changes the path and the extension of a crack beneath the surface.The first reason for this is that the compressive stress beneath the surface in all cases balances the Woodhead Publishing Limited,2014
The importance of measuring residual stresses 7 © Woodhead Publishing Limited, 2014 1.3 Effects of residual stresses The failures of composite materials are largely associated with residual stresses. The normal residual stress of the fi ber- matrix interface seriously infl uences fi ber matrix debonding and pull- out, the most prevalent failure mechanisms (Liu et al. , 1999; Nath et al. , 2000; Warrier et al. , 1999). Residual stress has also been proven to infl uence some other performance characteristics, including matrix cracking (Deve and Maloney, 1991), yield strength (Nakamura and Suresh, 1993; Zheng, 2000) and dimensional stability (Jain and Mai, 1996). Failures through fatigue, creep, wear, stress corrosion cracking, fracture, buckling, etc., are mainly caused by residual stresses. Furthermore, residual stresses regularly lead to dimensional instability, an example of which is distortion following heat treating or machining of a part. In parts without external loads, residual stresses can be located. All manufacturing processes can bring about residual stresses, and correlated loads are exaggerated with residual stresses. Residual stresses are subtle as they compensate equilibrium and thus remove all outer traces of their presence. It is necessary to be aware of residual stresses in all engineering structures in which safety factors are a problem, as residual stresses contribute to failures. Residual stresses brought about by different manufacturing processes can be predicted or modeled and much research is underway in this area (Prime, 1999a,b). The discharges of residual stresses cause deformation, be it an inconspicuous process leading to the formation of a crack on a simple clay vase or an agitation of the Earth by a massive earthquake which causes great destruction. It is generally very diffi cult to predict failures resulting from residual stresses. The existence of residual stresses has a signifi cant effect on the integrity of the mechanical components at work, in such circumstances as a nuclear reactor over an extended period of time, or in systems of high security- sensitivity, such as an airplane. The existence of residual tensile stresses close to the surface is regarded as one of the major contributing factors leading to the slow and ongoing formation of cracks in parts of objects that are exposed to radiation. Containers that are welded and sealed completely (Masubushi, 1980; Prime 1999a,b) and those containing nuclear waste, the radioactive level of which continues to be dangerously high for many centuries, are more subject to these sorts of residual stresses. Machining by turning, which is an operation performed on most shafts and rods, generally causes tensile residual stresses close to the surface (Brinksmeier et al. , 1982). These stresses are destructive to fatigue life under the pressure of cyclic loads. In addition, the compressive residual stress present close to the surface has been proven to lengthen fatigue life and prevent stress corrosion cracking (Cheng and Finnie, 2007). Not only does residual stress affect the formation of surface cracks, it also changes the path and the extension of a crack beneath the surface. The fi rst reason for this is that the compressive stress beneath the surface in all cases balances the
⊙ Residual stresses in composite materials tensile stress close to the surface.Thus it significantly slows down the growth of a crack as it reaches the region of compressive stress.The second reason is that with the extension of the crack,the stiffness or compliance of the area changes, resulting in the release of the previously trapped-in load.An example of the first case would be a surface crack,which is exposed to uni-axial tension.Such a crack will enlarge and infiltrate a plate,as the width of the crack reaches a size of nearly four times its thickness(Raju and Newman,1979).However,a crack loaded by the same outer pressure from above,with a considerable residual stress beneath its surface,will extend more quickly on the surface,with a width to depth ratio greater than ten.Consequently,the crack takes longer to penetrate the object, despite the fact that the component continues to lose strength with the further extension of the crack upon the surface.For a pressurized vessel under such circumstances,any leakage taking place may be a sign of a quickly growing crack (Finnie et al.,1990). It is usual for parts to become deformed upon welding or heat-treatment during manufacturing processes,and the understanding of this is an indicator of the extent to which engineers are experienced (Prime,1999a b).Analyses of the fundamental mechanics and measurement of residual stresses under different circumstances have substantially increased our knowledge about residual stresses throughout the past century,allowing us to assess and boost the integrity of current components.The behavior of materials and components is crucially affected by the existence of residual stresses. Residual stresses can lead to defects in composite structures,such as fiber waviness,cracking,delamination,warpage,dimensional instability and spring-in (Stamatopoulos,2011).Fiber waviness in uni-directional materials occurs when the fibers deviate from the average direction of the laminate,creating a pattern that can usually be mathematically represented by a sine wave (Fig.1.1).Fiber 0.1mm 1.1 Micrograph of a composite laminate showing fiber waviness (Parlevliet et al.,2007). Woodhead Publishing Limited,2014
8 Residual stresses in composite materials © Woodhead Publishing Limited, 2014 tensile stress close to the surface. Thus it signifi cantly slows down the growth of a crack as it reaches the region of compressive stress. The second reason is that with the extension of the crack, the stiffness or compliance of the area changes, resulting in the release of the previously trapped- in load. An example of the fi rst case would be a surface crack, which is exposed to uni- axial tension. Such a crack will enlarge and infi ltrate a plate, as the width of the crack reaches a size of nearly four times its thickness (Raju and Newman, 1979). However, a crack loaded by the same outer pressure from above, with a considerable residual stress beneath its surface, will extend more quickly on the surface, with a width to depth ratio greater than ten. Consequently, the crack takes longer to penetrate the object, despite the fact that the component continues to lose strength with the further extension of the crack upon the surface. For a pressurized vessel under such circumstances, any leakage taking place may be a sign of a quickly growing crack (Finnie et al. , 1990). It is usual for parts to become deformed upon welding or heat- treatment during manufacturing processes, and the understanding of this is an indicator of the extent to which engineers are experienced (Prime, 1999a,b). Analyses of the fundamental mechanics and measurement of residual stresses under different circumstances have substantially increased our knowledge about residual stresses throughout the past century, allowing us to assess and boost the integrity of current components. The behavior of materials and components is crucially affected by the existence of residual stresses. Residual stresses can lead to defects in composite structures, such as fi ber waviness, cracking, delamination, warpage, dimensional instability and spring- in (Stamatopoulos, 2011). Fiber waviness in uni- directional materials occurs when the fi bers deviate from the average direction of the laminate, creating a pattern that can usually be mathematically represented by a sine wave ( Fig. 1.1 ). Fiber 1.1 Micrograph of a composite laminate showing fi ber waviness (Parlevliet et al. , 2007)