Propagation Curve Research Articles

The relationship between crack front twisting, plastic zone and [formula omitted] curve of fatigue cracks in AA2024-T3

While fatigue crack growth is inherently a three-dimensional challenge, it is often modelled in two dimensions for simplicity. This study explores the relationship between the two-dimensional primary plastic zone (PPZ) on the surface of specimens and the three-dimensional twisting of the crack front leading to a slanted crack front. Fatigue crack growth experiments were conducted using 2-mm-thick MT-160 AA2024-T3 sheet specimens in both L-T and T-L crack orientations. High-resolution digital image correlation (HR-DIC) was employed to capture the PPZ within the surface displacement data and correlate its morphology with the twisting angle of the slanted crack front.Further, this study investigates how the twisting of the crack front affects the crack propagation curve, represented as da/dN−ΔK, by examining its influence on the mixed-mode I/II/III loading state along the crack front. Here, we utilize finite element simulations to derive a mapping function that adjusts ΔK to ΔKeqv, accounting for the twisted crack front caused mixed-mode loading conditions. The modified da/dN−ΔKeqv curves for both L-T and T-L orientations demonstrated similar behaviour, suggesting that differences in their crack front twisting may explain the discrepancies observed in their traditional da/dN−ΔK crack propagation curves.

Phase change in a one-dimensional functionally graded material

Functionally graded materials (FGMs) are a class of materials with engineered microstructure to achieve spatial variation in properties so as to serve a desired function. While FGMs have been well-researched for their structural properties, there is a lack of investigation of FGMs in solid-liquid phase change heat transfer processes. A well-designed functionally graded phase change material (FG-PCM) may overcome some of the well-known limitations of the phase change process. In order to investigate this possibility, this work presents a theoretical model to predict phase change propagation in a one-dimensional FG-PCM containing an arbitrary spatial variation in thermal conductivity, thermal diffusivity and latent heat. The problem is solved using the method of eigenfunction expansion to determine the temperature distribution, wherein, spatial variation in thermophysical properties listed above is accounted for by deriving a first-order matrix ordinary differential equation in the coefficients of the series solution. Results are found to correctly reduce to the well-known Stefan solution under special conditions. The impact of variation in thermophysical properties is investigated in detail. It is found that while spatial variation in thermal conductivity and latent heat has a significant effect on the rate of phase change, the impact of the thermal diffusivity function is negligible for realistic values of the Stefan number. The effect of the Stefan number governing this problem on the rate of melting is investigated. The nature of phase change under linear (1+aξ), polynomial (1+aξn) and exponential (eaξ) functional forms of thermophysical properties is investigated. It is shown that an appropriate choice of these spatial functions may help overcome the well-known self-limiting nature of phase change and produce a nearly-linear phase change propagation curve. For example, results show 33% increase in phase change propagation for a linear (1+5ξ) variation in thermal conductivity compared to baseline. The theoretical tools developed here may help design and optimize functionally graded PCMs towards improved phase change heat transfer in applications of practical interest.

The popular gene of hot event: A hot event propagation mechanism based on information coupling and information energy interaction

Recently, the research on the propagation of hot events has received widespread attention. By analyzing the data of hot events and the data of the common events in the same period on the network, we found that hot events usually break out quickly and opinion leaders and cluster behaviors exist in their propagation process. At the same time, the media public opinion fields of reporting hot events overlap and promote each other. Based on the common factors that drive an event to become a hot event, we used the heat calculation formula and entropy method to put forward the propagation model of hot events based on information coupling and information energy interaction. In the model, the coupling values of different event information are quantified based on the information fragment coupling effect. The heat calculation formula is used to dynamically adjust the propagation probability of different individuals in the propagation process of hot event, and the sensational effect threshold is introduced based on the overall energy value of the event. Finally, we used the real social relationship networks to simulate the evolution propagation process of the hot events, and compared it with the crawling real propagation curve of the events. The proposed model provides a good supplement for the study of the hot events.

Signal propagation curve for digital television broadcast network in Nigeria

Signal propagation curve for digital television broadcast network in Nigeria

Identification of the parameters contained in a cyclic cohesive zone model for fatigue crack propagation

Cyclic cohesive zone models provide a useful tool to describe fatigue driven crack propagation, covering a wide range of engineering applications. For a proper use of these models, particular attention must be devoted to the correct calibration of the parameters contained, considering that some of these can be characterized by a large variability and/or by the absence of a precise physical meaning so that they are not amenable to a direct measurement. This paper proposes a robust inverse analysis procedure, to investigate the identifiability of the model parameters governing the fatigue induced damage evolution, in a recently proposed cyclic cohesive zone model. A novel control for compact test specimens providing more meaningful experimental information is proposed. The identification problem is formulated by considering fatigue crack propagation curve and deformations measurements in a discrete number of points of the specimen surface as input data of the inverse algorithm. The finite element operator, adopted to simulate the experimental tests, has been substituted by a proper calibrated meta model to reduce the computational cost of the forward operator and, thus, to solve the inverse problem in a stochastic context through Monte Carlo like procedures. Representative results, obtained starting from virtual data affected by different levels of noise, are reported to highlight the identifiability of the model parameters on the basis of the experimental data adopted. Indications regarding the minimum number of measurements needed to make the inverse problem well-posed are also provided, supporting possible planning of measurements setups for laboratory investigations.

An Insight on the Estimation of Wave Propagation Constants in an Orthogonal Grid of a Simple Line-Supported Periodic Plate Using a Finite Element Mathematical Model

This article describes the propagation of free waves in a two-dimensional periodic plate using the finite element (FE) method. The advantage of periodic structure analysis is that all the dynamic properties of a finite structure are derived from a single phase-frequency curve or surface. Infinite plates are considered as a combination of periodic plates on an orthogonal array of simple, evenly spaced line supports. A single periodic unit of the system is represented by a more accurate high-precision arbitrary triangular shallow shell FE model to find the plane wave frequency in terms of the propagation constants of the 2D periodic plate. Only the purely propagating waves with no attenuation are considered here. The natural frequency of the infinite plate was obtained for different propagation constants in the two directions of the plate. The results are compared with the literature data. The bounding frequency of the propagation surface is compared to the data published from single square and rectangular plates with different edge boundary conditions. In addition, the natural frequency of the plate supported by finite line support with spans Nx (x-direction) and Ny (y-direction) is compared with the frequency obtained from the propagation curve by the discretization principle. The comparison is seen to be very close. It is found that the current PS-FEM approach can be used to generate dispersion relations with reasonable accuracy.

Robust Determination of Fatigue Crack Propagation Thresholds from Crack Growth Data.

The robust determination of the threshold against fatigue crack propagation is of paramount importance in fracture mechanics based fatigue assessment procedures. The standards ASTM E647 and ISO 12108 introduce operational definitions of based on the crack propagation rate and suggest linear fits of logarithmic – test data to calculate . Since these fits typically suffer from a poor representation of the actual curvature of the crack propagation curve, a method for evaluating using a nonlinear function is proposed. It is shown that the proposed method reduces the artificial conservativeness induced by the evaluation method as well as the susceptibility to scatter in test data and the influence of test data density.

Effect of pH on the corrosion and crack growth behavior of the ZK60 magnesium alloy

To investigate the effect of pH on corrosion and fatigue crack growth of ZK60 magnesium alloy, the corrosion and fatigue crack growth experiments with cyclic sinusoidal waveform in PBS with pH 5.2, 7.4 and 9.0 were performed. With the increase of pH, the integrity and compactness of the protective layer increased as well as Mg3(PO4)2, reducing the channels for Cl− and hydrogen to contact the magnesium matrix which inhibited pitting and crack growth rate in LI stage. In LII stage, the effect of pH was weakened and the slope of crack propagation curve decreased.

Prediction of Fatigue Crack Growth Behaviour in Ultrafine Grained Al 2014 Alloy Using Machine Learning

The present work investigates the relationship between fatigue crack growth rate (da/dN) and stress intensity factor range (∆K) using machine learning models with the experimental fatigue crack growth rate (FCGR) data of cryo-rolled Al 2014 alloy. Various machine learning techniques developed recently provide a flexible and adaptable approach to explain the complex mathematical relations especially, non-linear functions. In the present work, three machine algorithms such as extreme learning machine (ELM), back propagation neural networks (BPNN) and curve fitting model are implemented to analyse FCGR of Al alloys. After tuning of networks with varying hidden layers and number of neurons, the trained models found to fit well to the tested data. The three tested models are compared with each other over the training as well as testing phase. The mean square error for predicting the FCG of cryo-rolled Al 2014 alloy by BPNN, ELM and curve fitting methods are 1.89, 1.84 and 0.09 respectively. While the ELM models outperform the rest of models in terms of training time, curve fitting model showed best performance in terms of accuracy over testing data with least mean square error (MSE). In terms of local optimisation, back propagation neural networks excel the other two models.

Impacto geopolítico, económico y sanitario del SARS-Cov-2 (COVID-19) a nivel mundial: Taiwán un referente mundial después de sus experiencias en la epidemia de SARS-Cov-1

La pandemia del SARS-CoV-2 (COVID-19) superó a 10 veces más la propagación del virus que el SARS-CoV-1 del 2002. Causó una gran recesión económica que se sumó a la crisis económica del 2020. Colapsó los sistemas públicos y privados de los países desarrollados que subestimaron la virulencia y mutación viral, especialmente en Italia y España, resultando en 372.756 casos confirmados y 16231 muertes (4.3% de casos totales) a nivel global. Países como Singapur y Taiwán, desarrollaron sus protocolos con la epidemia del SARS-Cov-1, y demostraron al mundo como ser eficientes a una amenaza biológica mundial. Actualmente, sus estrategias permiten aplanar la curva de propagación del COVID-19, y fueron referentes mundiales para afrontar la pandemia localmente. Por otro lado, China Continental, compite con EE.UU. por el poder económico y político de las regiones, así como el desarrollo de una vacuna para finales del 2020. En cuanto a las estrategias e indicadores asociados al COVID-19 y su impacto político en salud y en la economía local, Ecuador, localizado en Sudamérica, con 17 millones de habitantes, y un PIB de 9.5% destinado a la salud pública, se convirtió en el segundo país con mayor prevalencia de casos (n=981) y se ubicó en el puesto 26º en el mundo. Las estrategias parciales tomadas a nivel nacional, sumado a la falta de cultura preventiva de la sociedad ecuatoriana, propagaron rápidamente el COVID-19. La falta de gestión de insumos médicos, y la escasez del personal médico (15 médicos por cada 10.000 habitantes), así como déficit de camas hospitalarias (tasa=1.4/1.000 habitantes/nivel nacional [0.8 del sector público], por debajo de Cuba con 5.4) y pruebas de PCR-RT, pone en peligro el sistema de salud de colapsarse, por el aumento exponencial del virus COVID-19 analizado hasta la 6ta semana del impacto local. Sin embargo, el análisis de PIB% entre Ecuador (PIB=9.5%) y Taiwán (PIB=6.3%), y las medidas estratégicas empleadas, rectifican que el sistema universal de salud de Taiwán, es muy eficiente en estrategias y respuestas a la emergencia del COVID-19. Estrategias de Taiwán han sido reflejadas en nuestro entorno para aplanar la curva epidemiológica y reducir el gasto público local. 

Practical method for parametric array source evaluation at 120 kHz frequency range in the near-field region

A parametric array is a non-linear conversion process that can generate a narrow beam of low-frequency sound with a small aperture. One of the challenging issues with a parametric array is precise measurement of the sound field generated. In particular, near the transducer, it is not easy to measure the sound field generated by a parametric array precisely, because the amplitude of the difference frequency wave is much lower than the amplitude of the primary wave. In this study, the practical issues that should be considered in the design of near-distance experiments with a parametric array are examined. Limiting effects were examined, and their associated characteristics were identified by numerical simulations. Experiments were performed in a water tank (18 x 12 x 10 m) to assess these characteristics, using a custom-designed acoustic filter; the beam pattern and propagation curve of the difference frequency wave generated by the parametric array were measured and compared with simulated data.

High cycle fatigue behavior and life prediction for additively manufactured 17-4 PH stainless steel: Effect of sub-surface porosity and surface roughness

The high potential of additive manufacturing (AM) techniques offers novel opportunities and unexplored design freedom. However, typical internal defects and poor surface quality inherent to AM process not only cause a lower fatigue resistance, but also more scatter in fatigue data; thus, hindering adoption of AM to fatigue critical applications. This study investigates the effect of surface quality and sub-surface porosity on high cycle fatigue behavior of 17-4 precipitation hardening (PH) stainless steel (SS) fabricated using laser beam powder bed fusion (LB-PBF) process. Parts were fabricated in three conditions: net-shape (NS) specimens, oversized specimens, and cylindrical rods. The oversized specimens and cylindrical rods were, respectively, further shallow machined (SM) and deep machined (DM) to the dimensions and geometry of net-shape specimens. The population of defects was investigated via optical microscopy of polished sections, X-ray micro-CT scan analysis, and fractography of fracture surfaces after fatigue tests. The fatigue crack growth (FCG) properties were generated at three stress ratios of R=-1,0.1,0.7 to determine the Kitagawa-Takahashi diagram and propagation curve. The polished sections showed the presence of large sub-surface, close-to-surface pores in the NS specimens, while SM and DM conditions had smaller and more uniformly distributed porosity. Critical defects detected on the fracture surfaces were small pores in machined specimens, and relatively large surface irregularities in NS specimens. Machining process, both in SM and DM conditions, enhanced the fatigue performance of the material as compared to that of NS condition. However, in terms of level of machining allowance, no further enhancement in fatigue performance was observed for DM specimens as compared to that of SM ones. Fatigue assessment for both net-shape and machined conditions was obtained performing FCG simulations based on the typical surface features and volumetric defects. Simulation results yielded correct estimates for both net-shape and machined specimens.

Investigating propagation curves of electric field intensity of Jigawa Medium Frequency Radio Transmitter

This study investigates the variations in the electric field intensity of Jigawa Medium Frequency (MF) radio signal along some radio routes using propagation curve. It also compares the propagation curves due to measured field intensity with those predicted by GRWAVE software using the ground electrical conductivity of the routes. The need to predict propagation curves using GRWAVE software and compare same with empirical curves to ascertain the adequacy and suitability of the predicted curves to characterize MF propagation in Northern Nigeria is the motivation for this study. Electric field intensity data were acquired with the aid of Potomac electric field intensity meter and a Garmin 38Global Position System (GPS) receiver registered both coordinates and elevations along the routes. Theoretical equation was used to deduce the values of ground electrical conductivity from the measured field intensity and the values were used along with the transmitter configuration in GRWAVE software to compute the predicted field intensity. Results reveal experimental propagation curves are fairly higher compared to predicted curves. At 30 km from the transmitter, the values of measured and predicted electric field strength are 1.30 and 1.06 mV/m along Tundun Wada route, 1.50 and 1.11 mV/m along Azare route, 1.40 and 1.15 mV/m along Kefin Hausa route, 1.41 and 1.13 mV/m along Kogin Maikaho route, 1.26 and 1.03 mV/m along Kundun route, 1.50 and 1.11 mV/m along Fulani route, and 1.25 and 1.11 mV/m along Dutse Kan route. Therefore GRWAVE software can be used to predict propagation curves suitable for MF propagation in Northern Nigeria using the ground electrical conductivity of the terrain.Key word: Propagation curve, electric field intensity, ground electrical conductivity, ground wave.

The effect of a chin-down maneuver after esophagectomy on oropharyngeal swallowing pressure measured using high-resolution manometry

ObjectiveTo elucidate the effects of a chin-down maneuver using high-resolution manometry (HRM) to measure pharyngeal swallowing pressure (SP) after esophagectomy. MethodsWe evaluated 9 of 16 patients who underwent esophagectomy featuring gastric tube reconstruction and three-field lymph node dissection (3FL) in our Department of Gastroenterological Surgery from September 2015 to June 2016. We compared all parameters of the neutral and chin-down positions using HRM to measure the maximum SP at the velopharynx, meso-hypopharynx, and upper esophageal sphincter (UES) and the duration of lowered SP at the UES, the distance from nostrils to the boundary between hypopharynx and UES and to derive SP and SP propagation curves at various distances from the nostrils. ResultsCompared to that at the neutral position, the maximum SP at the velopharynx was significantly lower in the chin-down position (p<0.05); however, SP at the meso-hypopharynx and UES did not differ significantly. The duration of lowered SP at the UES was significantly prolonged in the chin-down position and the distance from nostrils to the boundary between hypopharynx and UES was significantly shortened representing the elevation of the larynx, respectively (p<0.05, p<0.01). On the SP propagation curve for males, the times to SP peaks at 13, 16, 17, and 18cm from the nostrils were significantly prolonged (all p<0.05) in the chin-down position. ConclusionChin-down positioning after esophagectomy/3FL may improve bolus passage by prolonging the duration of lowered SP at the UES, possibly by enhancing laryngeal elevation.

Experimental Investigation of Oil Recovery from Tight Sandstone Oil Reservoirs by Pressure Depletion

Oil production by natural energy of the reservoir is usually the first choice for oil reservoir development. Conversely, to effectively develop tight oil reservoir is challenging due to its ultra-low formation permeability. A novel platform for experimental investigation of oil recovery from tight sandstone oil reservoirs by pressure depletion has been proposed in this paper. A series of experiments were conducted to evaluate the effects of pressure depletion degree, pressure depletion rate, reservoir temperature, overburden pressure, formation pressure coefficient and crude oil properties on oil recovery by reservoir pressure depletion. In addition, the characteristics of pressure propagation during the reservoir depletion process were monitored and studied. The experimental results showed that oil recovery factor positively correlated with pressure depletion degree when reservoir pressure was above the bubble point pressure. Moreover, equal pressure depletion degree led to the same oil recovery factor regardless of different pressure depletion rate. However, it was noticed that faster pressure drop resulted in a higher oil recovery rate. For oil reservoir without dissolved gas (dead oil), oil recovery was 2–3% due to the limited reservoir natural energy. In contrast, depletion from live oil reservoir resulted in an increased recovery rate ranging from 11% to 18% due to the presence of dissolved gas. This is attributed to the fact that when reservoir pressure drops below the bubble point pressure, the dissolved gas expands and pushes the oil out of the rock pore spaces which significantly improves the oil recovery. From the pressure propagation curve, the reason for improved oil recovery is that when the reservoir pressure is lower than the bubble point pressure, the dissolved gas constantly separates and provides additional pressure gradient to displace oil. The present study will help engineers to have a better understanding of the drive mechanisms and influencing factors that affect development of tight oil reservoirs, especially for predicting oil recovery by reservoir pressure depletion.

A New Crack Propagation Model Based on the Notch Analysis Methodology

In this paper, the fatigue crack propagation model of the metal structure is studied, and a new crack propagation rate model is proposed. Compared with the traditional method, only the nominal applied stress and the critical fracture stress are considered in the new method, and the new one is much easier and more efficient. By analyzing the 2024-T351 and 7075-T6 aluminum alloy materials test data, the new model is validated and the results are compared with the classical method of crack propagation. The result shows the new model has a similar trend with the existing crack propagation curve, and provides a better description for the low rate and high rate area, it also shows a strongly practicability.

Crack-Size Measurement of Additive Manufactured Plastics Based on the DCPD Method

Abstract Additive manufacturing offers the possibility of producing novel plastic products, which can be unique and complex, especially when the use of load-bearing components leads to a periodic load. Therefore, plastic components must also be examined for a sufficient service life. The aspects of crack initiation and crack propagation are particularly important. In this regard, a significant parameter is the crack propagation curve, for whose determination a continuous crack-size measurement is required. This article addresses how far the Direct Current Potential Drop (DCPD) method can be applied on additive manufactured plastics in order to make a statement about the fracture mechanical behavior of the materials. For this reason, the surfaces of compact tension (CT) specimens were coated with an electrically conductive layer using two different coating methods. Referring to this, experimental investigations were carried out in regard to the applicability of the DCPD method. Overall, two different coating methods were tested with experimental investigations. The experiments showed that the methods of galvanization and specimen coating enabled the application of the DCPD method to additive manufactured plastics. Furthermore, fracture mechanical investigations were carried out. In this context, crack propagation curves were determined by using both methods, and typical fracture mechanics parameters, e.g., threshold value, ΔKI,th, and stress-intensity factor at unstable crack propagation, ΔKIC, were identified.

Mechanism Study on Elevation Effect of Blast Wave Propagation in High Side Wall of Deep Underground Powerhouse

In view of the influence of blasting excavation in the deep burial underground powerhouse on the dynamic disturbance and blasting vibration of side wall and surrounding rock, the blasting vibration test method is often used for on‐site monitoring and control. Taking the blasting excavation of the high side wall of an underground powerhouse of a hydropower station as the engineering background, a long‐term blasting vibration test is carried out on the site. The measuring points are arranged along the elevation direction and horizontal direction of the high side wall of the powerhouse. Through analyzing and comparing the blasting vibration velocity values extracted from a large number of on‐site measured data in the elevation direction, an interesting phenomenon is found. The measured vibration velocity of the rock anchor beam in the area far away from the blasting is greater than that in the area near the blasting, and the vibration velocity after the casting of the rock anchor beam is greater than that before the casting. In order to avoid the randomness and contingency of the measured data, based on the blasting parameters, loading quantity, and rock mechanical characteristics used in the field, the elevation effect of the numerical model of the underground powerhouse is established by using the dynamic finite element software. By comparing the numerical simulation and the on‐site monitoring of the elevation direction vibration velocity at the same location, it is found that the two have the same law, which verifies the reliability of the numerical calculation model. By changing the elevation and horizontal distances to select the measuring points in the numerical model, the propagation curve of the blasting vibration of the high side wall of the underground powerhouse in the elevation direction is obtained and the wave propagation phenomenon and the local elevation amplification effect of blasting vibration velocity in the side wall of the powerhouse are found. By means of changing the morphology characteristics of the rock anchor beam, a numerical calculation model of the rock anchor beam before casting is established, and the blasting vibration velocity in the elevation direction of the same measuring point as the original model is extracted. The analysis and comparison results show that the “whiplash effects” caused by the reflection superposition of the convex morphology characteristics of the rock anchor beam on the blast wave and the vibration response of the rock mass at the step part is the main factor for the elevation effect. The fluctuation phenomenon of the vibration velocity in the elevation direction is caused by the natural frequency and the main vibration mode of the high side walls, and the reflection superposition of the convex geomorphology characteristics of the rock anchor beam will aggravate this fluctuation phenomenon. Therefore, in the construction of deep underground powerhouses, attention should be paid to the blasting construction and support design of the rock anchor beam.

A new tool for modelling the decompression behaviour of CO2 with impurities using the Peng-Robinson equation of state

Carbon capture and storage is considered as promising technique by the scientific community to reduce CO2 emissions and is composed by three different stages: CO2 capture, transportation and storage. The capturing plant has to be installed where processes involving large CO2 emissions, as power generation from fossil fuel, concrete and iron plants are present. The captured CO2 in real applications will be likely a CO2 dominated mixture with a content of several impurities, depending on the capture process which presence affects the thermo-physical properties of the pure CO2, especially increasing the vapour pressure curve. Such behaviour plays an important role in the control of the ductile fracture, whenever the CO2 is transported using pipelines. In the unfortunate event of a pipeline failure, the study of the pipeline decompression can be useful to estimate whether the fracture will remain confined or will propagate. The residual pressure acting on the crack tip of the pipeline represents the energy source governing the fracture’s propagation. The pressure profile is given by the expansion wave, which propagates along the pipeline during the fracture. In the literature, it is common practice to model the expansion wave by assuming one-dimensional isentropic decompression. In this study, a new code developed by the authors for modelling the decompression behaviour in the fluid is presented. The code is based on the Peng-Robinson equation of state with the Peneloux correction correlation matching the density of pure components to experimental data. The sound velocity in the two-phase region has been modelled with the method proposed by Nichita et al., which increase the accuracy of prediction with respect to the most popular Wood’s method. The code was validated against experimental and numerical data relating to hydrocarbon gas mixtures and CO2-rich mixtures. In particular, the results obtained for the hydrocarbon gas mixture decompression have been compared with experimental data and the predictions calculated by the software GASDECOM, in order to assess the accuracy of the code, that was then utilized to calculate the expansion wave curves for CO2-rich mixtures. The results obtained have been compared with experimental data and with predictions generated by the GERG2008 equation of state, found in literature. The simulated expansion wave curves show a good agreement with the experimental data for the tested compositions, especially for the plateau characterising the two-phase transition of rich gas compositions. The plateau corresponds to the saturation pressure, which is a key parameter for the fracture propagation control in CO2 pipelines, since the material toughness required to prevent a propagating ductile fracture is determined by applying the condition that the fracture propagation curve does not cross this value.

Temporal Evolution of the Gamma-ray Burst Afterglow Spectrum for an Observer: GeV–TeV Synchrotron Self-Compton Light Curve

Abstract We numerically simulate the gamma-ray burst (GRB) afterglow emission with a one-zone time-dependent code. The temporal evolutions of the decelerating shocked shell and energy distributions of electrons and photons are consistently calculated. The photon spectrum and light curves for an observer are obtained taking into account the relativistic propagation of the shocked shell and the curvature of the emission surface. We find that the onset time of the afterglow is significantly earlier than the previous analytical estimate. The analytical formulae of the shock propagation and light curve for the radiative case are also different from our results. Our results show that even if the emission mechanism is switching from synchrotron to synchrotron self-Compton, the gamma-ray light curves can be a smooth power law, which agrees with the observed light curve and the late detection of a 32 GeV photon in GRB 130427A. The uncertainty of the model parameters obtained with the analytical formula is discussed, especially in connection with the closure relation between spectral index and decay index.