Residual Stress Evaluation of Short-Fiber Reinforced Plastics by X-Ray Diffraction

Transcription

1 dvanced Materials Research Online: ISSN: , Vol 996, pp doi:148/wwwscientificnet/mr Trans Tech Publications, Switzerland Residual Stress Evaluation of Short-Fiber Reinforced Plastics by X-Ray Diffraction Keisuke Tanaka 1, a *, Yuuki Koike 1,b and Yoshiaki kiniwa,c 1 Departent of Mechanical Engineering, Meijo University, Nagoya, Japan Departent of Mechanical Engineering, Yokohaa National University, Yokohaa, Japan a ktanaka@eijo-uacjp, b koiyu51@gailco, c akiniwa@ynuacjp Keywords: Residual stress, X-ray diffraction, Short-fiber reinforced plastics, Microechanics bstract The X-ray diffraction ethod is used to evaluate the residual stress in injection-olded plates of short-fiber reinforced plastics (SFRP) ade of crystalline theroplastics, polyphenylene sulphide (PPS), reinforced by carbon fibers with 3 ass% The stress in the atrix in the skin layer was deterined using Cr-Kα radiation with the sin ψ ethod The X-ray evaluation of stress in carbon fibers was not possible because of high texture new ethod was proposed to evaluate the acrostress in SFRP fro the easureent of the atrix stress ccording to icroechanics analysis of SFRP, the atrix stresses in the fiber direction and perpendicular to the fiber direction, and shear stress can be expressed as linear functions of the applied (acro-) stresses in the fiber direction and perpendicular to the fiber direction, and shear stress The proportional constants are naed stress-partitioning coefficients Using skin-layer strips cut parallel, perpendicular and 45 to the olding direction, the stress in the atrix was evaluated under the uniaxial applied stress and the stress-partitioning coefficients of the above equations were deterined Once the relations between the acrostress and atrix stress are established, the acrostress in SFRP can be evaluated fro the easureents of the atrix stresses using X-rays Introduction Short-fiber reinforced plastics (SFRP) are expected to be used ore widely in order to reduce the weight of ground vehicles, because the injection olding process akes high-rate and econoical production possible Their application in fatigue-sensitive coponents is steadily increasing [1,] Since the residual stress ight have a big influence on the fatigue strength, the nondestructive evaluation of residual stresses existing in SFRP structures is significant to grantee the structural integrity against fracture and fatigue X-ray diffraction techniques can evaluate the stress in crystalline aterials, and will be applied to SFRP when the atrix or fiber is ade of crystalline aterials Polyphenylene sulphide (PPS) is a versatile teperature and cheical resistant, inherently flae retardant crystalline theroplastics [3] PPS is usually reinforced by short carbon fibers or glass fibers, and the injection olding process is used in producing parts of ground vehicles In the present paper, the X-ray diffraction ethod is used to evaluate the stress in injection-olded SFRP ade of PPS reinforced with carbon fibers Based on the orientation of carbon fibers, injection olded plates (IMP) can be odeled as three-layered laella where the core layer is sandwiched by skin layers The stress in the atrix in the skin layer was evalauted fro back diffractions of (), (111) of PPS using Cr-Kα radiation with sin ψ ethod new ethod is proposed to evaluate the residual stress of SFRP fro the atrix stress deterined by X-rays X-Ray Evaluation of Stress in SFRP X-Ray Stress Evaluation of Coposites The sin ψ ethod is coonly used to deterine the surface stress in single-phase polycrystalline aterials which have rando orientation under the condition of plane stress The stress can be deterined fro the slope of the linear relation of diffraction angle θ and sin ψ by ultiplying the stress constant K as follows [4]: This is an open access article under the CC-BY 4 license (

2 95 Residual Stresses IX ( ) ( sin ) σ x = K M, M = θ ψ (1) For ultiphase aterials, the X-ray ethod can detect the ean stress in each phase, and the acrostress is deterined fro the phase stresses obtained for all constituent phases using a rule of ixture For two-phase aterials like SFRP, the acrostress, σ, is deterined fro the atrix stress σ and the fiber stress ( 1 f ) f σ as σ = σ + σ f, f where f is the volue fraction of fibers [4] To deterine the acrostress using above equation, the phase stress in both phases need to be known The X-ray ethod of stress evaluation is difficult to apply to aorphous glass fibers or highly textured carbon fibers Therefore, we propose a new ethod to deterine the acrostress only fro the atrix stress Macrostress Evaluation of SFRP fro Matrix Stress By odeling fibers in SFRP as prolate spheroids, the stresses in atrix and fiber phases can be calculated as a function of the applied stress based on icroechanics as described in ppendix ssuing the plane stress state, the atrix stresses parallel and perpendicular to fibers, σ 1 and σ, and the atrix shear stress, 1, are related to the applied (acro-) stresses parallel and perpendicular to fibers, σ 1 and σ, and the atrix shear stress, 1, as follows: = α55 1, σ = α σ + α σ, σ = α σ + α σ, (5) where coefficients αij indicate the atrix stress partitioned fro the applied stress, and can be naed stress-partitioning coefficients In the present paper, these coefficients are deterined experientally, and afterward they will be used to evaluate the acrostress fro the atrix stress deterined by X-rays Experiental Procedure Materials and Speciens The experiental aterial was SFRP ade of PPS reinforced with 3 ass% of carbon fibers The volue fraction deterined fro density was Test speciens were achined fro injection-olded plate (IMP) with the thickness of 1 IMP can be regarded as three-layer laella with the core layer of 15 sandwiched by skin layers [5] The fiber direction of the skin layer is parallel to the olding direction and that of the core layer perpendicular to it The skin layer plate (SLP) with the thickness of 4 was produced by achining IMP fro one side only Strip speciens with 1 width and 55 length were cut out fro SLP with the longitudinal directions parallel, perpendicular, and 45 to the olding direction, and they are called MD (olding direction), TD (transverse direction), and 45 speciens, respectively X-Ray Conditions The characteristic X-rays of Cr-Kα radiation was used for stress evaluation The X-ray equipent used was a high power X-ray generator and parallel bea optics The only peak with a strong intensity found between and 16 was the doublet of () and (111) of PPS at θ=353 [6,7] We use this peak for stress deterination, although the sensitivity is because of low diffraction angle The sin ψ ethod using the side-inclination arrangeent was used for stress deterination The linear absorption coefficients of PPS and SFRP deterined experientally were 154 c -1 and 118 c -1, respectively [5] The X-ray penetration depth was at ost 15 µ fro the surface Deterination of Stress-Partitioning Coefficients of SRPR The load was applied stepwise to three types of SFRP speciens, MD, TD and 45, in the longitudinal direction The atrix stress was easured in the longitudinal and transverse directions of each specien as shown in Fig 1, where the suffixes 1 and indicate the stresses in the fiber direction and the perpendicular directions, and the () (3) (4)

3 dvanced Materials Research Vol suffix ± 45 indicates the angle ± 45 to the fiber direction For MD specien, the applied stress isσ 1 and coefficients α11, α 1 can be deterined fro the atrix stresses, σ1, σ, as a function of the applied stress Siilarly, coefficients α1, α can be deterined fro the relation between the atrix stress and the applied stress obtained for TD specien For 45 specien, the applied stress σ 45 induces the shear stress 1 The shear stress in the atrix, 1, is deterined fro the easured values of σ 45, σ 45 + in the atrix as ( + ) = σ σ (6) Fro the above two equations, the coefficient of α55 is deterined by ( + ) α = = σ σ σ (7) Fig 1 Two directions of X-ray stress deterination for each type of FRP specien under applied stress Experiental Results and Discussion Stress Measureent of PPS Fig shows the θ-sin ψ diagras obtained fro PPS speciens at various applied stresses Linear regression lines give good approxiation to the data for each stress The slope of sin ψ diagras changes linearly with the applied stress as shown in Fig 3, where the bars attached to each data points indicate 683% confidence liit of the linear regression The stress constant was deterined fro the change of the slope of sin ψ diagras with the applied stress as K = 14 7 MPa deg Matrix Stress of SFRP under pplied Stress The atrix stress was deterined in two directions of MD, TD and 45 speciens under the applied stress ll data show good linear relations in θ-sin ψ diagras, and the atrix stress was calculated fro the slope of linear regression lines ultiplied by the stress constant Fig 4 shows the relation between the atrix stress and the applied stress obtained in two directions for MD, TD and 45 speciens The bars attached to each data point indicate 683% confidence liit of the linear regression It is very interesting to notice that the atrix stress at unloaded state is close to zero Theral icrostress of the atrix due to the isatch in the coefficient of theral expansion coefficient between atrix and fiber is negligible in the skin layer, because the penetration depth of X-rays is shallow and the stress relieved near the free surface This is very iportant for X-ray stress easureent, otherwise the theral icrostress should be subtracted fro the easured atrix stress to evaluate the acrostress of SFRP The stress coponents perpendicular to the surface are also negligible for SFRP Under loading, the atrix stress changes linearly with the applied stress for all cases Fro the slope of linear regression, the following relations were obtained, and the stress-partitioning coefficients are deterined as follows: σ = 35σ + 31σ, (8) σ = σ + σ, (9) = (1)

4 954 Residual Stresses IX Fig θ -sin ψ diagra of PPS under applied stress Fig 3 Changes of slope with applied strain for PPS (a) MD specien (b) TD specien Fig 4 Matrix stress as a function of applied stress for three types of SFRP (c) 45 specien

5 dvanced Materials Research Vol Proposed Method of Residual Stress Measureent of SFRP Residual stresses on the surface of SFRP coponents are expected to be biaxial plane stress state Once the fiber direction is known at the easureent points, the acrostress, σ 1 and σ, parallel and perpendicular to fibers can be deterined fro the easureents of the atrix stresses, σ and σ, in two directions by 1 1 α σ α σ σ1 = α α α α α σ α σ σ = α α α α , (11) (1) The shear stress, 1, is deterined fro the atrix stresses, σ + 45, σ 45, easured in two directions ±45 to the fiber direction by using the following equation: ( + ) = σ σ α The application of the present ethod to SFRP coponents in ground vehicles will be conducted in the future Suary new ethod was proposed to evaluate the acrostress in SFRP fro the easureent of the atrix stress The atrix stress in crystalline theroplastics PPS was deterined with the sin ψ ethod (1) The atrix stresses in the fiber direction and perpendicular to the fiber direction, and the shear stress in SFRP are expressed as the proportional functions of the applied (acro-) stresses and the proportional constants were deterined experientally () Once the fiber direction is known at the easureent position of the stress in SFRP, the residual stress in the skin layer of SFRP can be evaluated fro the atrix stress deterined by X-rays in four directions: the directions parallel, perpendicular and ±45 to the fibers ppendix Microechanics of SFRP Fig 5 shows a odel SFRP where fibers are represented by prolate spheroids aligned along the olding direction The stress in atrix and fiber phases can be calculated as a function of the applied stress based on icroechanics of Eshelby s ellipsoidal inclusions [8] cobined with the Mori-Tanaka ean stress theory [9] The atrix is assued to have isotropic elastic constant C, and the fiber has orthogonally anisotropic elastic constant Cf When the stress, σ (=σ ) is applied to SFRP, the strain, e, of the atrix without fibers is related to the applied stress In SFRP, the atrix stress is perturbed by fibers and the additional stress, σ%, is introduced in the atrix The strain, e%, associated to the stress σ% The atrix stress, σ, is expressed by σ = σ + % σ = C ( e + e% ) (14) Since the s additional strain, e, is introduced in fiber phase due to the isatch of elastic constant, the ean stress in the fiber phase is f σ = σ + % σ = C f ( e + e% + e) (15) The fiber stress can be expressed by equivalent inclusions with the eigen strain e*, as follows [8]: C (16) f ( e + e% + e) = C ( e + e% + e e ) The additional strain, e, is related to eigen strain e* through e = S e (17) where S is Eshelby s tensor ccording to Mori-Tanaka ean stress theory, the voluetric integral of the additional stress, σ%, is zero Fro this condition, the strain, e%, is deterined as follows: % (18) ( ) e = f e e (13)

6 956 Residual Stresses IX Fig 5 Calculation odel of elastic deforation of SFRP (The fibers are aligned along the olding direction, x1 axis) By substituting Eqs (15), (16) into Eq (14), the eigen strain is deterined as 1 e [( C f C ) {( 1 f ) S fi} C ] ( C f C ) e e (19) The atrix stress is given fro Eqs (1), (16), (17) as follows: 1 σ = C ( e + e% ) = C [ I f ( S I ) ] e = C [ I f ( S I ) ] C σ F σ () The above equation gives the relation between the atrix stress and the applied stress atrix representation of the above relation is For the case of plane stress, the atrix stress are given expressed as In the ain context, the applied stress is expressed as σ in stead of σ It is interesting to note that the applied noral stresses perpendicular and parallel to fibers induce only noral stresses perpendicular and parallel to the fibers, but not the shear stress, in the atrix References σ 1 σ 1 α11 α1 α1 σ α 1 α α3 σ σ 3 α 1 α3 α σ 3 = α α α σ = α σ + α σ, σ = α1σ 1 + α σ, 1 = α55 1 [1] J Karger-Kocsis, Fracture of short-fiber reinforced theroplastics, in: K L Reifsnider (Ed), pplication of Fracture Mechanics to Coposite Materials, L, Elesevier Science Pub, sterda, (1989) [] J F Mandell, Fatigue behavior of short fiber coposites aterials, in: K L Reifsnider (Ed), Fatigue of Coposites, Elesevier Science Pub, sterda, (199) [3] J Karger-Kocsis and K Friedlich, Microstructural details and the effect of testing conditions on the fracture toughness on injection-olded poly(phenylene-sulphide) coposites, Journal of Materials Science, Vol (1987) (1) () (3) (4)

7 dvanced Materials Research Vol [4] K Tanaka, K Suzuki and Y kiniwa, Evaluation of Residual Sresses by X-Ray Diffraction, Yokendo, Tokyo (6) [5] K Tanaka, S Tokoro, N Egai and Y kiniwa, X-ray residual stress easureent of short-fiber reinforced plastics, Proceeding of the 47 th Syposiu of X-Ray Studies of Mechanical Behavior of Materials, The Society of Materials Science, Japan, (13) [6] B J Tabor, E P Magre and J Boon, The crystal structure of poly-p-phenylene sulphide, European Polyer Journal, Vol 7 (1971) [7] J S Chung, J Bodzich and P Chee, Effects of theral history on crystal structure of poly(phenylene sulphide), Journal of Materials Science, Vol 7 (199) [8] J D Eshelby, The deterination of the elastic field of an ellipsoidal inclusion, and related probles, Proceedings of Royal Society, London, Vol 41 (1957) [9] T Mori and KTanaka, verage stress in atrix and average energy of aterials with isfitting inclusions, cta Metallugica, Vol 1 (1973)