Destructive techniques in the measurement of residual stresses 19 Bert and Thompson(1968)developed the theoretical basis for relating measured strains to residual stresses in orthotropic materials applying an approximate calculation procedure.Later a precise formulation for uniform through-thickness residual stresses in a limited class of orthotropic materials was proposed by Schajer and Yang (1994).Sicot and Gong (2003,2004)made an approximate analysis of the residual stresses in orthotropic composite laminates using the incremental hole-drilling method.An exact formulation of the through-hole method enabling the measurement of uniform through-thickness residual stresses in a generic orthotropic laminate was published by Pagliaro and Zuccarello (2007).The effects of macro-scale residual stresses acting on symmetrical orthotropic laminates can also be considered using this method. The hole-drilling method most commonly uses strain gages,which must be correctly positioned relative to the hole.Although not so widely used,optical methods have an advantage over strain gages in that positioning of the hole is less important.A technique has been developed to determine residual stresses in orthotropic materials using Moire interferometry for any alignment of Moire gratings (Cardenas-Garcia,2005).Dual beam shearography yields the in-plane strain directly,since the axes of symmetry in the measured fringe pattern correspond to the axes of the principal stresses.In spite of this advantage over Moire interferometry,measuring residual stress in orthotropic materials using shearography combined with the hole-drilling technique appears to be limited.Qualitative measurements have been obtained on composite panels.In an effort to speed up measurement,micro-indentation (whereby a small indent is pressed into the measurement surface)has been used instead of the hole-drilling process (Hung,1999),but this process again has only yielded qualitative measurements. All the current analytical methods used with hole drilling assume the material within a single ply to be homogeneous,and are therefore unable to resolve the micro-scale residual stresses within a heterogeneous ply.However,since fibers are cut when a hole is drilled into a composite laminate,residual stress is released at the cut and an elastic response occurs in the adjoining material.It is thus potentially possible to use the hole-drilling technique for measuring micro-scale residual stress in GFRP.The region over which a significant elastic response takes place is,nonetheless,extremely small (Nairn,1997).Since the maximum diameter of E-glass reinforcement fibers is often less than 27um,measurements must be taken within a small distance of the edge of the hole (Corning,2003),which causes problems if the smallest commercially available strain gages are used.If extremely small special gages were developed to overcome the problem of sensitivity,they would simply introduce another problem due to self-heating. GFRP is not a good conductor of heat,therefore the localized heating effect of such a small gage becomes important(Reid,2009). Fiber optic Bragg gratings have been employed for measuring residual stresses in a composite laminate in a modified version of the hole-drilling method,with the Woodhead Publishing Limited,2014
Destructive techniques in the measurement of residual stresses 19 © Woodhead Publishing Limited, 2014 Bert and Thompson (1968) developed the theoretical basis for relating measured strains to residual stresses in orthotropic materials applying an approximate calculation procedure. Later a precise formulation for uniform through- thickness residual stresses in a limited class of orthotropic materials was proposed by Schajer and Yang (1994). Sicot and Gong (2003, 2004) made an approximate analysis of the residual stresses in orthotropic composite laminates using the incremental hole- drilling method. An exact formulation of the through- hole method enabling the measurement of uniform through- thickness residual stresses in a generic orthotropic laminate was published by Pagliaro and Zuccarello (2007). The effects of macro- scale residual stresses acting on symmetrical orthotropic laminates can also be considered using this method. The hole- drilling method most commonly uses strain gages, which must be correctly positioned relative to the hole. Although not so widely used, optical methods have an advantage over strain gages in that positioning of the hole is less important. A technique has been developed to determine residual stresses in orthotropic materials using Moiré interferometry for any alignment of Moiré gratings (Càrdenas-Garcìa, 2005). Dual beam shearography yields the in- plane strain directly, since the axes of symmetry in the measured fringe pattern correspond to the axes of the principal stresses. In spite of this advantage over Moiré interferometry, measuring residual stress in orthotropic materials using shearography combined with the hole- drilling technique appears to be limited. Qualitative measurements have been obtained on composite panels. In an effort to speed up measurement, micro- indentation (whereby a small indent is pressed into the measurement surface) has been used instead of the hole- drilling process (Hung, 1999), but this process again has only yielded qualitative measurements. All the current analytical methods used with hole drilling assume the material within a single ply to be homogeneous, and are therefore unable to resolve the micro- scale residual stresses within a heterogeneous ply. However, since fi bers are cut when a hole is drilled into a composite laminate, residual stress is released at the cut and an elastic response occurs in the adjoining material. It is thus potentially possible to use the hole- drilling technique for measuring micro- scale residual stress in GFRP. The region over which a signifi cant elastic response takes place is, nonetheless, extremely small (Nairn, 1997). Since the maximum diameter of E-glass reinforcement fi bers is often less than 27 μ m, measurements must be taken within a small distance of the edge of the hole (Corning, 2003), which causes problems if the smallest commercially available strain gages are used. If extremely small special gages were developed to overcome the problem of sensitivity, they would simply introduce another problem due to self- heating. GFRP is not a good conductor of heat, therefore the localized heating effect of such a small gage becomes important (Reid, 2009). Fiber optic Bragg gratings have been employed for measuring residual stresses in a composite laminate in a modifi ed version of the hole- drilling method, with the
20 Residual stresses in composite materials Bragg gratings embedded within the laminate (Guemes and Menendez,2002) They avoid the self-heating effect,but are too long to be used for measuring stress relief around individual fiber breaks.In addition.the analytical method used to interpret the measured response must accommodate the stiffening effect of the transducer.It seems unlikely that reliable measurements of the stress reliefrelative to a fiber break could be made with this method(Reid,2009). The use of optical methods present two important problems that are prevalent, irrespective of the instrumentation technique employed (Reid,2009).The first significant problem arises from the introduction of residual stresses in drilling the hole.The strains measured are those resulting from the release of residual stress superimposed on those caused by the hole-drilling process,and the two sets of strains cannot be separated from each other.EDM would minimize the residual stresses caused by making the hole,but only where the fibers and matrix are conductive,and unfortunately neither the fiber nor the matrix in GFRP satisfies this criterion(Reid,2009).It might be possible to avoid the introduction of residual stresses during hole drilling through the micro-indentation process (Hung,1999),but the interpretation of the strain measurements would be complicated by the heterogeneity of the material at small scales (Reid,2009). Thus the hole-drilling method,and variations of it,cannot be directly used or adapted for use in finding the micro-scale residual stresses in uni-directional GFRP(Reid,2009). Buchmann et al.(2000)describe a novel approach to simulating the thermal spraying process by modeling a moving heat source combined with the material transfer and deposition process.Their quantified stresses and deformations agree with experimental residual stress measurements by the advanced hole-drilling method.According to Prasad et al.(1987),the semi-destructive hole-drilling technique for measuring residual stresses is well established for isotropic materials and they have made attempts to extend this method to orthotropic composite materials.Pagliaro and Zuccarello (2007)dealt with the development and application of the through-hole drilling method for residual stress analysis in orthotropic materials. Balalov etal.(2007)discussed in detail the main features inherent in a simplified approach to residual stress determination in cylindrical shells and tubes with external diameters of not less than 60 mm,by combining the hole-drilling method and reflection hologram interferometry.Stefanescu et al.(2006)presented results advancing and improving the usefulness,accuracy and efficiency of incremental center-hole drilling as a method of measuring close-to-surface residual stress fields.Shokrieh and Kamali (2005)studied the residual stresses in thermoset polymer composites.Shokrieh and Ghasemi (2007a,b)presented a new method (simulated hole-drilling method)for calculating the calibration factors for measuring the residual stresses in different material systems.Baldi (2007) analyzed the problem of residual stress determination in an orthotropic material using the hole-drilling technique combined with non-contact,full-field optical Woodhead Publishing Limited,2014
20 Residual stresses in composite materials © Woodhead Publishing Limited, 2014 Bragg gratings embedded within the laminate (Guemes and Menéndez, 2002). They avoid the self- heating effect, but are too long to be used for measuring stress relief around individual fi ber breaks. In addition, the analytical method used to interpret the measured response must accommodate the stiffening effect of the transducer. It seems unlikely that reliable measurements of the stress relief relative to a fi ber break could be made with this method (Reid, 2009). The use of optical methods present two important problems that are prevalent, irrespective of the instrumentation technique employed (Reid, 2009). The fi rst signifi cant problem arises from the introduction of residual stresses in drilling the hole. The strains measured are those resulting from the release of residual stress superimposed on those caused by the hole- drilling process, and the two sets of strains cannot be separated from each other. EDM would minimize the residual stresses caused by making the hole, but only where the fi bers and matrix are conductive, and unfortunately neither the fi ber nor the matrix in GFRP satisfi es this criterion (Reid, 2009). It might be possible to avoid the introduction of residual stresses during hole drilling through the micro- indentation process (Hung, 1999), but the interpretation of the strain measurements would be complicated by the heterogeneity of the material at small scales (Reid, 2009). Thus the hole- drilling method, and variations of it, cannot be directly used or adapted for use in fi nding the micro- scale residual stresses in uni- directional GFRP (Reid, 2009). Buchmann et al . (2000) describe a novel approach to simulating the thermal spraying process by modeling a moving heat source combined with the material transfer and deposition process. Their quantifi ed stresses and deformations agree with experimental residual stress measurements by the advanced hole- drilling method. According to Prasad et al . (1987), the semi- destructive hole- drilling technique for measuring residual stresses is well established for isotropic materials and they have made attempts to extend this method to orthotropic composite materials. Pagliaro and Zuccarello (2007) dealt with the development and application of the through- hole drilling method for residual stress analysis in orthotropic materials. Balalov et al . (2007) discussed in detail the main features inherent in a simplifi ed approach to residual stress determination in cylindrical shells and tubes with external diameters of not less than 60 mm, by combining the hole- drilling method and refl ection hologram interferometry. Stefanescu et al . (2006) presented results advancing and improving the usefulness, accuracy and effi ciency of incremental center- hole drilling as a method of measuring close- to-surface residual stress fi elds. Shokrieh and Kamali (2005) studied the residual stresses in thermoset polymer composites. Shokrieh and Ghasemi (2007a,b) presented a new method (simulated hole- drilling method) for calculating the calibration factors for measuring the residual stresses in different material systems. Baldi (2007) analyzed the problem of residual stress determination in an orthotropic material using the hole- drilling technique combined with non- contact, full- fi eld optical
Destructive techniques in the measurement of residual stresses 21 methods.Schajer(1988,2007)and Schajer and Yang(1994)presented an effective procedure allowing for stable hole-drilling residual stress calculations using strain data from measurements taken at many small increments of hole depth.Schajer (1988,2007)described the use of Tikhonov regularization to reduce the noise sensitivity characteristic of a fine-increment calculation,and combined this mathematical procedure with the Morozov criterion to identify the optimal amount of regularization that balances the competing tendencies of noise reduction and stress solution distortion. Schajer and Yang (1994)used the hole-drilling method to measure residual stresses in an orthotropic material.Sicot et al.(2003)presented a new method for measuring residual stress in composite laminates,using three cooling conditions to produce different residual stress levels.Shokrieh and Ghasemi (2007a,b) determined that the calibration factors for orthotropic plates are based on an exact solution method.Bert and Thompson (1968)and Lake et al.(1970)extended a method to include orthotropic materials by introducing new coefficients of calibration,and investigated the applicability of the semi-destructive hole-drilling technique to the experimental determination of residual stresses in relatively thin rectangular orthotropic materials. 2.4.2 The incremental hole-drilling method The incremental hole-drilling method takes account of the non-uniformity of the stress distribution through the thickness.The basic principle for the calculation of stresses is the same as with the hole-drilling method,but in this case drilling is performed gradually.The measured strains are processed by an appropriate model and the residual stresses are calculated (Oettel,2000;Parlevliet et al.,2006;Sicot etal.,2003). The incremental,high-speed hole-drilling and circular-milling technique has several advantages that make it suitable for measuring residual stress on coating composites.The measuring set-up is comparatively small(Fig.2.2),offers high flexibility and can be applied to a variety of complex machine parts.The measurement of surface strains by means of strain gages is a well-known technique with a reasonably high accuracy (errors are in the range of 2 to 5%(Hausler et al., 1987)).The stepwise removal of material in increments of 5 to 20um leads to a good depth resolution.In comparison with the conventional hole-drilling method, the combination of high-speed drilling and circular milling (Fig.2.2)reduces the mechanical loading of the material at the bottom of the bore-hole,the plastic deformation in the center of the hole,and the thermal input into the material. Therefore,manipulation of the intrinsic residual stresses during measurement is reduced and the accuracy of results is increased.Difficulties in applying the hole- drilling method are mainly due to preparation of the surface by grinding without influencing the residual stresses,and the adhesion of the strain gages to the surface (Wenzelburger et al.,2006). Woodhead Publishing Limited,2014
Destructive techniques in the measurement of residual stresses 21 © Woodhead Publishing Limited, 2014 methods. Schajer (1988, 2007) and Schajer and Yang (1994) presented an effective procedure allowing for stable hole- drilling residual stress calculations using strain data from measurements taken at many small increments of hole depth. Schajer (1988, 2007) described the use of Tikhonov regularization to reduce the noise sensitivity characteristic of a fi ne- increment calculation, and combined this mathematical procedure with the Morozov criterion to identify the optimal amount of regularization that balances the competing tendencies of noise reduction and stress solution distortion. Schajer and Yang (1994) used the hole- drilling method to measure residual stresses in an orthotropic material. Sicot et al . (2003) presented a new method for measuring residual stress in composite laminates, using three cooling conditions to produce different residual stress levels. Shokrieh and Ghasemi (2007a,b) determined that the calibration factors for orthotropic plates are based on an exact solution method. Bert and Thompson (1968) and Lake et al . (1970) extended a method to include orthotropic materials by introducing new coeffi cients of calibration, and investigated the applicability of the semi- destructive hole- drilling technique to the experimental determination of residual stresses in relatively thin rectangular orthotropic materials. 2.4.2 The incremental hole- drilling method The incremental hole-drilling method takes account of the non- uniformity of the stress distribution through the thickness. The basic principle for the calculation of stresses is the same as with the hole- drilling method, but in this case drilling is performed gradually. The measured strains are processed by an appropriate model and the residual stresses are calculated (Oettel, 2000; Parlevliet et al ., 2006; Sicot et al ., 2003). The incremental, high- speed hole- drilling and circular- milling technique has several advantages that make it suitable for measuring residual stress on coating composites. The measuring set- up is comparatively small ( Fig. 2.2 ), offers high fl exibility and can be applied to a variety of complex machine parts. The measurement of surface strains by means of strain gages is a well- known technique with a reasonably high accuracy (errors are in the range of 2 to 5% (Häusler et al ., 1987)). The stepwise removal of material in increments of 5 to 20 μ m leads to a good depth resolution. In comparison with the conventional hole- drilling method, the combination of high- speed drilling and circular milling ( Fig. 2.2 ) reduces the mechanical loading of the material at the bottom of the bore- hole, the plastic deformation in the center of the hole, and the thermal input into the material. Therefore, manipulation of the intrinsic residual stresses during measurement is reduced and the accuracy of results is increased. Diffi culties in applying the holedrilling method are mainly due to preparation of the surface by grinding without infl uencing the residual stresses, and the adhesion of the strain gages to the surface (Wenzelburger et al ., 2006)
22 Residual stresses in composite materials D/2 Strain gage 2.2 Measurement set-up of the incremental-step,circular hole-drilling and milling method(pneumatic turbine,motors for three-axis position control,LCD-camera,strain gage data acquisition),and illustration of the method(Wenzelburger et al.,2006).Notation:z, depth;d diameter of bore hole;D,diameter of circle on which strain gage rosette is positioned. A disadvantage of the incremental hole-drilling method is that the size of a typical strain gage rosette is two to four times larger than the diameter of the hole,making the area covered by the rosette very large compared to the stress field(Fig.2.3).Another frequent problem is eccentric drilling,such as when the hole is not drilled exactly at the center of the rosette.The hole-drilling method has been applied in combination with Moire interferometry,holographic interferometry and speckle interferometry,as well as in combination with finite element modeling for determination of the residual stresses.Incremental hole- drilling can be utilized to study residual stresses in between adjacent plies,but optimal drilling and translation speeds must be found (Margelis et al.,2010; Parlevliet et al.,2006). Tsouvalis et al.(2009)proposed a new method of calibration showing how finite element analysis can be used to determine the correlation coefficients,and take account of the effects of changes in the hole geometry,which they reported can cause a significant error in the experimental data.Sicot et al.(2003,2004) described an application of the incremental hole-drilling method to measure residual stress in a uni-directional and a [0/90].carbon/epoxy laminate with thicknesses of the order of I mm,measuring tensile and compressive residual stresses in the fiber direction and transverse direction up to a magnitude of about 100 MPa.Sicot et al.(2004)studied the effect of two experimental parameters: the depth of each drilled increment and the effect of the relative position of the strain gages compared with the radius of the hole drilled. Manson and Seferis (1992)applied the PSL technique to develop a method to evaluate the distribution of process-induced residual stresses,making use of a strain gage that was attached to the laminate.Grant et al.(2002)provided a practical guide to achieving better measurements,drawing together some Woodhead Publishing Limited,2014
22 Residual stresses in composite materials © Woodhead Publishing Limited, 2014 A disadvantage of the incremental hole- drilling method is that the size of a typical strain gage rosette is two to four times larger than the diameter of the hole, making the area covered by the rosette very large compared to the stress fi eld ( Fig. 2.3 ). Another frequent problem is eccentric drilling, such as when the hole is not drilled exactly at the center of the rosette. The hole- drilling method has been applied in combination with Moiré interferometry, holographic interferometry and speckle interferometry, as well as in combination with fi nite element modeling for determination of the residual stresses. Incremental holedrilling can be utilized to study residual stresses in between adjacent plies, but optimal drilling and translation speeds must be found (Margelis et al ., 2010; Parlevliet et al ., 2006). Tsouvalis et al . (2009) proposed a new method of calibration showing how fi nite element analysis can be used to determine the correlation coeffi cients, and take account of the effects of changes in the hole geometry, which they reported can cause a signifi cant error in the experimental data. Sicot et al . (2003, 2004) described an application of the incremental hole- drilling method to measure residual stress in a uni- directional and a [0/90] s carbon/epoxy laminate with thicknesses of the order of 1 mm, measuring tensile and compressive residual stresses in the fi ber direction and transverse direction up to a magnitude of about 100 MPa. Sicot et al . (2004) studied the effect of two experimental parameters: the depth of each drilled increment and the effect of the relative position of the strain gages compared with the radius of the hole drilled. Manson and Seferis (1992) applied the PSL technique to develop a method to evaluate the distribution of process- induced residual stresses, making use of a strain gage that was attached to the laminate. Grant et al . (2002) provided a practical guide to achieving better measurements, drawing together some 2.2 Measurement set- up of the incremental- step, circular hole-drilling and milling method (pneumatic turbine, motors for three- axis position control, LCD-camera, strain gage data acquisition), and illustration of the method (Wenzelburger et al. , 2006). Notation: z, depth; d0 , diameter of bore hole; D, diameter of circle on which strain gage rosette is positioned
Destructive techniques in the measurement of residual stresses 23 X Hole G X/2 个利 G3 2.3 Relative location of the hole and the strain gages(Sicot et al., 2004).Notation:R.,hole radius;R,radius of outside strain gage;R radius of middle strain gage;G,and G,first and third strain gages; X,gage length background to the technique,discussing the current standards and highlighting a number of key issues crucial to obtaining good measurements,based on input from UK experts and some of the findings from a recent UK hole-drilling residual stress inter-comparison exercise.Wenzelburger et al.(2006)described and compared the most common residual stress measurement techniques,focusing on incremental hole drilling and milling,and their application to industrial machine parts. 2.4.3 The deep hole-drilling method The deep hole-drilling (DHD)method is used to measure residual stress in isotropic materials,but it can also be applied to orthotropic materials such as thick laminated composites.For large structures,it is considered non-destructive, because a small hole does not affect the structural integrity.In this method,the formulation is mainly based on the calculation of the hole distortion in a plate under the effect of remote loading.For isotropic materials,there are suitable closed-form solutions;however,for orthotropic materials,a finite element approach should be used(Stamatopoulos,2011). Woodhead Publishing Limited,2014
Destructive techniques in the measurement of residual stresses 23 © Woodhead Publishing Limited, 2014 background to the technique, discussing the current standards and highlighting a number of key issues crucial to obtaining good measurements, based on input from UK experts and some of the fi ndings from a recent UK hole- drilling residual stress inter- comparison exercise. Wenzelburger et al . (2006) described and compared the most common residual stress measurement techniques, focusing on incremental hole drilling and milling, and their application to industrial machine parts. 2.4.3 The deep hole-drilling method The deep hole-drilling (DHD) method is used to measure residual stress in isotropic materials, but it can also be applied to orthotropic materials such as thick laminated composites. For large structures, it is considered non- destructive, because a small hole does not affect the structural integrity. In this method, the formulation is mainly based on the calculation of the hole distortion in a plate under the effect of remote loading. For isotropic materials, there are suitable closed- form solutions; however, for orthotropic materials, a fi nite element approach should be used (Stamatopoulos, 2011). 2.3 Relative location of the hole and the strain gages (Sicot et al. , 2004). Notation: Rt , hole radius; Rj , radius of outside strain gage; Rxj, radius of middle strain gage; G1 and G3, fi rst and third strain gages; Xj , gage length