The effect of temperature and loading rate on the mode II interlaminar fracture properties of a carbon fiber reinforced phenolic

The combined effect of varying loading rate and test temperature on the mode II Interlaminar fracture properties of a carbon fiber reinforced phenolic resin has been investigated. End notch flexure tests at room temperature have shown that this composite offers a relatively modest value of G_IIc^NL at non‐linearity and that its interlaminar fracture toughness decreases with increasing loading rate. As the test temperature is increased, the quasistatic value of G_IIc^NL increases steadily and the reduction in G_IIc^NL with loading rate becomes less dramatic. At temperatures approaching the glass transition temperature of the phenolic matrix, the interlaminar fracture toughness of the composite begins to increase sharply with crosshead displacement rate. A more detailed understanding of the effect of varying the test conditions on the failure mechanisms occurring at the crack tip of these interlaminar fracture specimens has been achieved using the double end notch flexure (DENF) geometry.     

Temperature and Loading Rate Effects on the Fracture Behaviour of Adhesively Bonded GFRP Nylon-6,6

The combined effect of varying test temperature and loading rate on the Mode II fracture toughness of plasma-treated GFRP Nylon-6,6 composites bonded using a silica-reinforced epoxy adhesive has been studied. End notch flexure tests have shown that the adhesive system used in this study offers a wide range of fracture energies that are extremely sensitive to changes in temperature and loading rate. Increasing the test temperature resulted in a substantial reduction in the Mode II fracture toughness of the adhesive, with the value of G_IIc at 60°C being approximately one-half of the room temperature value. In contrast, increasing the crosshead displacement rate at a given temperature has been shown to increase the value of G_IIc by up to 250%. Compression tests performed on bulk adhesive specimens revealed similar trends in the value of [sgrave]_y with temperature and loading rate. In addition, it was found that the plasma treatment employed in this study resulted in stable crack propagation through the adhesive layer under all testing conditions.

A more detailed understanding of the effect of varying temperature and loading rate on the failure mechanisms occurring at the crack tip was achieved using the double end notch flexure (DENF) geometry, which was considered in tandem with the fracture surface morphologies. Here, changes in the degree of matrix shear yielding and particle-matrix debonding were used to explain the trends in [sgrave]_y and G_IIc.     

Atomistic insight into ideal strength,fracture toughness,deformation, and failure mechanisms of magnetocaloric Fe2AlB2

The thermal and magnetic cycling of a magnetocaloric material degrades its mechanical properties and device performance. We used ab initio tensile and shear simulations to investigate the mechanical properties such as ideal strength, fracture toughness and deformation and failure mechanisms of Fe₂AlB₂ at finite strain. The weakest direction of Fe₂AlB₂ is [010], and the weakest slip system is (010)[100]. The ideal tensile strength (σ_m = 12.51 GPa) of Fe₂AlB₂ is less than its ideal shear strength (τ_m = 13.32 GPa). The strain energy difference (ΔE = −13 eV/f.u.) of Fe₂AlB₂ confirms cleavage fracture as its most plausible failure mode. The concomitant changes in the c-lattice parameter and Al–Al bond along the c-axis determine the ideal tensile strength of Fe₂AlB₂. Likewise, the subtle changes in the a-lattice parameter and Al–Al bond along the a-axis specify its ideal shear strength. The tensile strain induces a magnetic to nonmagnetic transition in Fe₂AlB₂ at the critical tensile strain (ε_c = 0.08). A similar transition occurs at the critical fracture strain (ε_cf = 0.48) due to shear deformation. The brittle nature of Fe₂AlB₂ is predicted by its anisotropic Poisson's ratios, strength ratio, and failure mode. The fracture toughness of Fe₂AlB₂ for mode I fracture is (K_Ic = 2.17 MPa m^1/2), mode II fracture is (K_IIc = 1.33 MPa m^1/2), and mode III fracture is (K_IIIc = 1.16 MPa m^1/2). The failure mechanism of Fe₂AlB₂ due to the tensile deformation is marked by the sharp and appreciable changes in the lattice parameters, bonding characteristics, and magnetic moment of Fe at the critical fracture strain (ε_cf = 0.44). This study provides a fundamental understanding of the mechanical behavior of Fe₂AlB₂ at the finite strain relevant to the cycling stability of the magnetocaloric Fe₂AlB₂.     

Temperature and loading rate effects in the mode II interlaminar fracture behavior of carbon fiber reinforced PEEK

The combined effect of varying loading rate and test temperature on the mode II interlaminar fracture properties of AS4/carbon fiber reinforced PEEK has been investigated. End notch flexure tests have shown that this thermoplastic‐based composite system offers a very high value of interlaminar fracture toughness at room temperature. Increasing the test temperature leads to a reduction in the mode II interlaminar fracture toughness of the composite, with the value at 150°C being approximately one half of the room temperature value. In contrast, increasing the crosshead displacement rate has been shown to increase the value of G_IIc by up to 25%. A more detailed understanding of the effect of varying temperature and loading rate on the failure mechanisms occurring at the crack tip of these interlaminar fracture specimens has been achieved using the double end notch flexure (DENF) geometry. Here, extensive plastic flow within the crack tip region was observed in all specimens. It is believed that the rate sensitivity of G_IIc reflects the rate‐dependent characteristics of the thermoplastic resin.     

Effect of temperature on fracture toughness of PC/ABS based on J-integral and hysteresis energy methods

The critical fracture toughness J_1c of the polycarbonate (PC)/acrylonitrile–butadiene–sty-rene (ABS) blend at different temperatures was obtained from ASTM E813-81, E813–87, and the recently developed hysteresis energy methods, respectively. The J_1c value increases with increase of the test temperature ranging from −60 to 70°C. the hysteresis energy method and the ASTM E813–81 method result in comparable J_1c values, while the ASTM E813–87 results in about 80–110% higher values. the critical initiation displacements determined from the plots of hysteresis energy and the true crack growth length vs. crosshead displacement are very close. This indicates that the critical initiation displacement determined by the hysteresis method is indeed the displacement at the onset of true crack initiation and the corresponding J_1c represents a physical event of crack initiation. The fracture toughness, K_1c value, based on linear elastic fracture mechanics (LEFM), was determined by using K_Q analysis (ASTM E399–78), and the obtained K_Q value decreases with the increase of the test temperature. The K_Q value is not the real LEFM K_1c value because the criterion of P_max/P_Q < 1.1 has not been satisfied. However, the corresponding J_Q obtained from the K_Q analysis is comparable to the J_1c obtained from the E813–81 method at lower temperature (−45 or −60°C), an indication of LEFM behavior at lower temperature. The various schemes and size criterion based on LEFM and the J-method are explored for the validity of J_1c and K_1c values. © 1996 John Wiley & Sons, Inc.     

Unusual Elastic and Mechanical Behaviors of Copper Phosphate Glasses with Different Copper Valence States

Elastic and mechanical properties such as Young's modulus E, Poisson's ratio ν, Debye temperature θ_D, Vickers hardness H_v, fracture toughness K_c, and fracture surface energies γ_f of yCuO_x·(100−y)P₂O₅ glasses (y= 45, 50, 55) with different copper valence states, i.e., R(Cu⁺) = Cu⁺/(Cu⁺+ Cu²⁺), at room temperature (humidity 64%) have been examined. The following features have been found: (1) the glass transition temperature (218–434°C), H_v (2.7–4.4 GPa), E (50.6–78.2 GPa), and θ_D (358–434 K) decrease largely with increasing R(Cu⁺); (2) the mean atomic volume, K_c (0.56–1.14 MPa·m^1/2), and γ_f (1.9–11.2 J·m⁻²) tend to increase with increasing R(Cu⁺); (3) 50CuO_x·50P₂O₅ glasses with R(Cu⁺) = 0.42 and 0.55 have a high resistance against crack formation in Vickers indentation tests and no crack is observed in the 45CuO_x·55P₂O₅ glass with R(Cu⁺) = 0.57 under an applied load of about 98 N. The results demonstrate that elastic and mechanical properties of yCuO_x·(100−y)P₂O₅ glasses depend strongly on the copper valence state and the CuO_x/P₂O₅ ratio. The unusal mechanical and elastic properties of copper phosphate glasses are well explained qualitatively by considering unique oxygen coordination and bonding states of Cu⁺ ions, i.e., lower coordination number and more covalent bonding compared with Cu²⁺ ions.     

Evaluation of adhesion and mechanical properties of plasma sprayed NiCrAl/Al2O3-13wt.%TiO2 coatings

Plasma sprayed NiCrAl/Al₂O₃-13wt.%TiO₂ coating was fabricated and annealed at 300–900 °C in air atmosphere. The Elastic modulus (E), micro-hardness (H_V) and fracture toughness (K_ca) were evaluated by Vickers Indentation Fracture technique. The microstructure was studied by scanning electron microscopy. It can be concluded that with the increasing of annealing temperature, E and H_V at the interface of Substrate/Bond layer (S/B) are firstly increased and retain the highest value at 600 °C then decreased with higher annealing temperatures due to the phase transformation. E of the ceramic coating rised initially with annealing temperature increasing, reached the highest value at 400 °C, and then decreased with the further increasing of the temperature. The K_ca of the S/B interface firstly increased as the heating temperature increasing, confirming the crack initiation resistance increasing after annealing with the temperature below 700 °C. However, the K_ca decreased for further annealing temperature, even lower than that of the as-sprayed coating. Thereby, a proper annealing temperature can improve the mechanical properties of the coating since the coating becomes denser, ceramic lamellar structure becomes ambiguous and cracks are partially healed.     

Thermal and scanning electron microscopy/energy‐dispersive spectroscopy analysis of styrene–butadiene rubber–butadiene rubber/silicon dioxide and styrene–butadiene rubber–butadiene rubber/carbon black–silicon dioxide composites

Silica as a reinforcement filler for automotive tires is used to reduce the friction between precured treads and roads. This results in lower fuel consumption and reduced emissions of pollutant gases. In this work, the existing physical interactions between the filler and elastomer were analyzed through the extraction of the sol phase of styrene–butadiene rubber (SBR)–butadiene rubber (BR)/SiO₂ composites. The extraction of the sol phase from samples filled with carbon black was also studied. The activation energy (E_a) was calculated from differential thermogravimetry curves obtained during pyrolysis analysis. For the SBR–BR blend, E_a was 315 kJ/mol. The values obtained for the composites containing 20 and 30 parts of silica per hundred parts of rubber were 231 and 197 kJ/mol, respectively. These results indicated an increasing filler–filler interaction, instead of filler–polymer interactions, with respect to the more charged composite. A microscopic analysis with energy‐dispersive spectroscopy showed silica agglomerates and matched the decreasing E_a values for the SBR–BR/30SiO₂ composite well. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 96: 2273–2279, 2005     

The local thermomechanical conditions and the fracture behavior of an injection‐molded poly(oxymethylene)

This work explores the fracture behavior of an injection‐molded engineering thermoplastic, poly(oxymethylene), POM. Lateral gated discs of 120 mm diameter and 1.5 mm thick were molded with variations of the melt temperature and injection flow rate. The local thermomechanical environment was characterized by computer simulations of mould filling phase. This also allows the computation of two thermomechanical indices related to the morphological state of the moldings. From the molded discs, double edge notched tensile (DENT) specimens were meticulously cut at different angles with respect to the flow direction and with distinct ligament lengths. The fracture tensile tests were performed at 2 mm/min at controlled room temperature. As the test configuration (specimen geometry) imposes a plane stress state, the stress intensity factor, K_I, was calculated as function of the processing conditions and orientation angle with respect to the flow direction. The K_I values and their degree of anisotropy are dependent upon processing conditions. Finally, the dependences of K_I values upon the thermomechanical indices (and therefore on the expected morphological state of the moldings) are established. POLYM. ENG. SCI. 46:181–187, 2006. © 2005 Society of Plastics Engineers     

Rectorite/thermoplastic polyurethane nanocomposites. II. Improvement of thermal and oil‐resistant properties

Organ‐rectorite/thermoplastic polyurethane (OREC/TPUR) nanocomposites were synthesized via melt intercalation. The dynamic mechanical properties by dynamic mechanical analysis (DMA), thermal and oil‐resistant properties were investigated. The results show that the storage modulus (E′), loss modulus (E″), and glass‐transition temperature (T_g) of the nanocomposites have an increase to some extent than those of pure TPUR. The thermal stability of nanocomposites was also studied in detail by thermal gravity analysis (TGA), which was higher than that of pristine TPUR matrix when the content of organic REC is at 2 wt %, and the decomposition temperature at 10% weight loss of OREC/TPUR is greatly increased up to 330°C from 315°C. Oil uptake of the composites is also significantly reduced in comparison with TPUR matrix, which is ascribed to the good barrier effect of nanosheets of OREC. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 96: 1165–1169, 2005     

Thermal Properties,Fracture Toughness and Water Absorption of Epoxy-Palm Oil Blends

Epoxidized palm oil (EPO) was blended with cycloaliphatic epoxide, epoxy novolac and diglycidyl ethers of bisphenol-A. The fracture toughness and thermal properties of epoxy/EPO blends were characterized using single-edge notched bending tests and differential scanning calorimetry. Increased EPO loading improved the fracture toughness (K _IC ) of the epoxy blends. The epoxy blends with higher EPO loading exhibited higher degree of conversion. The glass transition temperature (T _g ) of the epoxy blends shifted to higher temperature as the increasing of DSC heating rate. Water absorption caused T _g reduction of epoxy blends but it was determined that the water molecules absorbed were totally reversible.     

Thermal decomposition studies of Schiff‐base‐substitute polyphenol–metal complexes

The thermal behaviors of 2,3‐bis[(2‐hydroxyphenyl)methylene] diaminopyridine, oligo‐2,3‐bis[(2‐hydroxyphenyl)methylene] diaminopyridine, and some oligo‐2,3‐bis[(2‐hydroxyphenyl) methylene] diaminopyridine–metal complexes were studied in a nitrogen atmosphere with thermogravimetric analysis, derivative thermogravimetric analysis, and differential thermal analysis techniques. The decompositions of oligo‐2,3‐bis[(2‐hydroxyphenyl) methylene] diamino pyridine–metal complexes occurred in multiple steps. The values of the activation energy (E) and reaction order of the thermal decomposition were calculated by means of several methods, including Coats–Redfern, Horowitz–Metzger, Madhusudanan–Krishnan–Ninan, van Krevelen, Wanjun–Yuwen–Hen–Cunxin, and MacCallum–Tanner on the basis of a single heating rate. The most appropriate method was determined for each decomposition step according to a least‐squares linear regression. The E values obtained by each method were in good agreement with each other. It was found that the E values of the complexes for the first decomposition stage followed the order E_OHPMDAP–Ni > E_OHPMDAP–Cd > E_OHPMDAP–Cu > E_OHPMDAP–Fe > E_OHPMDAP–Zn > E_OHPMDAP–Co > E_OHPMDAP–Cr > E_HPMDAP > E_OHPMDAP. © 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2013     

Fatigue crack growth behavior and mechanism of closed‐cell PVC foam

The applicability of linear‐elastic fracture mechanics parameters (ΔK and K_max), elastic–plastic fracture mechanics parameter (ΔJ), and time‐dependent fracture mechanics parameter (C*) to characterize fatigue crack growth (FCG) rate of closed‐cell polyvinyl chloride foam was investigated in the present work. The effect of stress ratios (R = 0.1 and 0.4) on FCGs was observed when the ΔK, K_max and ΔJ were used as fracture mechanics parameters. As a fracture mechanics parameter that combines ΔK and K_max, the K* successfully characterized FCGs (da/dN) at R = 0.1 and 0.4. While, a time‐dependent fracture mechanics parameter (C*) successfully correlated da/dt of creep crack growth (CCG) test, but it failed to correlate da/dt of FCG tests. The FCGs at both R = 0.1 and 0.4 were cyclic dependent, while the CCG was time dependent. For cyclic‐dependent crack growth, the interaction between polymer‐chain scission and small scale crack‐tip blunting was the main mechanism, whereas the interaction between polymer‐chain pullout and large scale crack‐tip blunting dominated fracture process for time‐dependent crack growth. POLYM. ENG. SCI., 2013. © 2012 Society of Plastics Engineers     

Heterogeneous polyamide 66/syndiotactic polystyrene blends: Phase structure and thermal and mechanical properties

The structural and physical properties of polyamide 66 (PA66)/syndiotactic polystyrene (sPS) blends were studied with electron microscopy, wide‐angle X‐ray scattering (WAXS), differential scanning calorimetry (DSC), dynamic mechanical thermal analysis, and tensile creep, stress–strain, and impact measurements. Attention was primarily concentrated on blends with sPS weight fractions (w₂) in the range of 0 < w₂ ≤ 0.50. DSC and WAXS showed that the integral crystallinity of the PA66 and sPS components in the blends was virtually unaffected by the blend composition. Polymorphism of sPS was observed for blends with w₂ ≥ 0.50. Blends with 0.40 ≤ w₂ ≤ 0.60 consisted of partially cocontinuous components; otherwise, particles of the minority component were dispersed in the continuous majority component. The compatibilizer enhanced interfacial adhesion so that no debonding of the components in the fractured blends was observed. The compliance and creep rate of the blends at room temperature decreased proportionally to the sPS fraction; a corresponding increase in the storage modulus (E′) was observed in the 25–100°C interval. However, E′ (125°C) noticeably declined with w₂ and thus showed that sPS did not improve the dimensional stability of the blends at elevated temperatures. The yield strength consistently grew with w₂, whereas the yield strain dropped markedly; blends with w₂ ≥ 0.60 were brittle, showing very low values of the ultimate properties. The stress at break, strain at break, and tensile energy to break displayed some local maxima at 0.25 ≤ w₂ ≤ 0.30, whereas the tensile impact strength steeply decreased. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 96: 673–684, 2005     

Fracture toughness of particle filled fiber reinforced polyester composites

Fracture behavior of polyester composite systems, polyester mortar and glass fiber reinforced polyester mortar, was investigated in mode I fracture using single edge notched beams with varying notch depth. The beams were loaded in four-point bending. Influence of polymer content on the flexural and fracture behavior of polyester composites at room temperature was studied using a uniform Ottawa 20–30 sand. The polymer content was varied between 10 and 18% of the total weight of the composite. The flexural strength of the polyester mortar systems increase with increase in polymer content while the flexural modulus goes through a maximum. The critical stress intensity factor (K_IC) for the optimum polyester mortar (14%) was determined by two methods including a method based on crack mouth opening displacement. The K_IC for polyester mortar is linearly related to the flexural strength. Polyester mortar (18%) reinforced with 4% glass fibers was also investigated, and crack growth resistance curve (K_R) was developed with crack extension (Δa). A model has been proposed to represent the fracture toughness with change in crack length, K_R - Δa relationship, of fiber reinforced polyester composite.     

Toughening of epoxy thermosets with nano-sized or micron-sized domains of poly(ethylene oxide)-b-poly(butadiene-co-acrylonitrile)-b-poly(ethylene oxide) triblock copolymers synthesized using room temperature ester coupling reaction

Poly(ethylene oxide)-b-poly(butadiene-co-acrylonitrile)-b-poly(ethylene oxide) (PEO-b-PBN-b–PEO) triblock copolymers with three different compositions were synthesized from poly(ethylene glycol) methyl ethers and carboxylic acid-terminated poly(butadiene-co-acrylonitrile) (CTBN) by ester coupling reaction at room temperature. The PEO-b-PBN-b-PEO was incorporated into anhydride cured epoxy thermosets to improve the fracture toughness by the formation of either nano-sized spherical micelles or micron-sized vesicles. The polymer chemical structure was confirmed by Fourier transform infrared spectroscopy, nuclear magnetic resonance, and gel permeation chromatography. The morphology of PEO-b-PBN-b–PEO within the epoxy thermosets was investigated using a transmission electron microscope, an atomic force microscope, and a scanning electron microscope. Also, we conducted impact testing and plane-strain fracture toughness testing to evaluate the fracture toughness in terms of the impact strength and the critical stress intensity factors (K_IC) for the modified epoxy thermosets. The results revealed that all the PEO-b-PBN-b-PEO triblock copolymers are more effective in the toughening of epoxy thermoset compare to CTBN. We found that the 5 wt% PEO-b-PBN-b-PEO modified epoxy thermoset containing micron-sized vesicles exhibited the highest K_IC, which was 3.23 times as high as the K_IC of pristine epoxy thermoset. Besides, the glass transition temperature remained and the tensile modulus did not reduce remarkably when the amount of PEO-b-PBN-b-PEO added into epoxy was 5 wt%.     

Studies of thermal,mechanical properties,and kinetic cure reaction of carboxyl-terminated polybutadiene acrylonitrile liquid rubber with diepoxy octane

Epoxy resins, despite their unique properties, have limitations in many applications due to their low fracture toughness. One of the most effective methods to overcome this limitation is to use toughening agents, such as carboxyl terminated poly butadiene-acrylonitrile (CTBN) in the epoxy matrix. CTBN can react with various compounds, such as epoxies. In this study, we investigated the severity of CTBN sedimentation with di epoxy octane (DEO) in the presence basis catalysts. The studied of the physical properties of the synthesized copolymer in the presence of pyridine compared to other catalysts increases mechanical properties (248.43% elongation, 0.63 MPa strength, and 32 hardness with Shore A) and decreases the glass transition temperature (−45.1) of the copolymer. Investigated the cure kinetics of the CTBN-DEO reaction was in the presence of pyridine using a nonisothermal technique of differential scanning calorimetry, and the curing kinetic parameters, such as activation energy (E_a), pre-exponential factor (A), and rate constant (k), were calculated by different kinetic methods. The obtained curing kinetic values with different kinetic methods are well-matched, the E_a values are in the range of 91.3–97.1 kJ.mol⁻¹ and the A values are in the range of 0.48 × 10¹¹–1.51 × 10¹¹ S⁻¹.     

Effect of residual monomer content on some properties of a poly(methyl methacrylate)-based bone cement

Through this article, the degree of polymerization attainable in a commercial acrylic bone cement based on poly(methyl methacrylate) (PMMA) was investigated by differential scanning calorimetry (DSC) and gas chromatography (GC). The results obtained revealed a marked dependence between the maximum monomer conversion and the cure temperature. Specimens for the mechanical evaluation of the cement were subjected to two different cure conditions: one set of samples was allowed to cure at room temperature and an additional set was also postcured at 140°C for 2 h. The latter thermal treatment permitted one to discard the presence of the unreacted monomer in the hardened material. The effect of the unreacted monomer on the mechanical behavior was evaluated by measuring the flexural modulus (E), the compressive yield stress (σ_y), and the fracture toughness (K_IC). Samples prepared at room temperature for mechanical evaluation contained residual monomer which acts as a plasticizer of the matrix, increasing K_IC and decreasing E and σ_y. The cure temperature and mold di-mensions influence the amount of the residual monomer in the hardened material. Thus, differences in the values of the mechanical properties measured for the same commercial formulation may be attributed to a different mold dimension used in the test. © 1998 John Wiley & Sons, Inc. J Appl Polym Sci 69: 1367–1383, 1998     

Nonlinear time‐series analysis of optical signals to identify multiphase flow behavior in microchannels

This study provides an insight into the instability and irregularity of multiphase flows in microchannels. Using a homemade optical measuring system, time series related to two‐phase flow dynamics under different operating conditions, fluids, and channel lengths were collected and analyzed via a nonlinear characteristic parameter, Kolmogorov entropy (K_E). Our results reveal that higher K_E corresponds to unstable flow behavior, while lower K_E refers to steady flow behavior; higher K_E values appear at comparatively low or high gas flow rates, and most Taylor flow regime appeared at proper operating conditions with small K_E. An equation derived based on the definition of K_E is proposed to better understand K_E characteristics, which include bubble break‐up impact and gas/liquid flow rate ratio. Predictions from the proposed analytical equation agree with experimental results, suggesting that the equation effectively identifies unstable flows and can be used to ensure stable and predictable multiphase flows in microchannels. © 2016 American Institute of Chemical Engineers AIChE J, 63: 2378–2385, 2017     

Thermal stability and local atomic structure of (Na0.5K0.5)NbO3 doped BaTiO3 ceramics

Dielectric properties of x(Na_0.5K_0.5)NbO₃–(1−x)BaTiO₃ (x=0.00 and 0.06) specimens were investigated in terms of changes in local atomic structure, according to the phase transition by elevating the overall temperature. A 0.06(Na_0.5K_0.5)NbO₃–0.94BaTiO₃ (NKN–BT) specimen exhibited enhanced temperature stability along with an increased dielectric constant. The degree of reduction in tetragonality (c/a) at the Curie temperature was smaller in NKN–BT compared to that in pure BaTiO₃, as calculated by Rietveld refinement. From a comparison of the pre-edge region in the Ti K-edge, it was determined that the off-center displacement of the Ti atom was also raised to 13.4% through NKN substitution, with a change in local orientation from the [001] to the [111] directions. The substitution by NKN, which has a different ionic radius and electrical charge compared with BaTiO₃, causes structural distortion of the TiO₆ octahedra in the NKN–BT lattice, resulting in local polarization. These structural changes lead to the temperature stability of the dielectric constant and an overall improvement in the electrical properties of BaTiO₃.